Generation of a torsion wave and measuring its propagation velocity in the circumferential direction of arterial wall

Increased stiffness of the arteries has recently gained acceptance as a potential risk for cardiovascular and many other diseases. Pulse wave velocity (PWV) is widely used for estimating the stiffness of an artery. However, PWV is an indicator of average artery stiffness between two measuring points. In addition to measured PWV, the diameter and thickness are needed to calculate the elastic modulus of the artery. We present a new method to generate a torsion wave in the artery wall and measure its propagation speed in the circumferential direction of the artery. The elastic modulus of the artery can be calculated from the torsion wave velocity without the knowledge of the thickness of the artery, which is difficult to measure with accuracy.     

Image features in medical vibro-acoustography: in vitro and in vivo results

Vibro-acoustography is an imaging method based on audio-frequency harmonic vibrations induced in the object by the radiation force of focused ultrasound. The purpose of this study is to investigate features of vibro-acoustography images and manifestation of various tissue structures and calcifications in such images. Our motivation for this study is to pave the way for further in vitro and in vivo applications of vibro-acoustography. Here, vibro-acoustography images of excised prostate and in vivo breast are presented and compared with images obtained with other modalities. Resulting vibro-acoustography images obtained with a 3 MHz ultrasound transducer and at a vibration frequency of 50-60 kHz show soft tissue structures, tissue borders, and microcalcifications with high contrast, high resolution, and no speckle. It is concluded that vibro-acoustography offers features that may be valuable for diagnostic purposes.     

Group structure and the pointwise ergodic theorem for connected amenable groups

Let G be a connected amenable group (thus, an extension of a connected normal solvable subgroup R by a connected compact group $\text{K =}\text{G}\text{R}$). We show how to explicitly construct sequences {U_n} of compacta in G in terms of the structural features of G which have the following property: For any “reasonable” action G × L^p(X, μ) ↓ L^p(X, μ) on an L^p space, 1 <p < ∞, and any f ∈ L^p(X, μ), the averages

$\text{A}{}_{\mathrm{n}}\text{f=}\text{1}\text{|U}{}_{\mathrm{n}}\text{|}\text{∫}\text{U}{}_{\mathrm{n}}\text{T}{}_{\mathrm{g}}{}^{\mathrm{?1f}}\text{dg (|E|=}\text{left Haar measure in}\text{G)}$

converge in L^p norm, and pointwise μ-a.e. on X, to G-invariant functions $\text{f1}$ in L^p(X, μ). A single sequence {U_n} in G works for all L^p actions of G. This result applies to many nonunimodular groups, which are not handled by previous attempts to produce noncommutative generalizations of the pointwise ergodic theorem.     

Passive all-optical force clamp for high-resolution laser trapping

Optical traps are useful for studying the effects of forces on single molecules. Feedback-based force clamps are often used to maintain a constant load, but the response time of the feedback limits bandwidth and can introduce instability. We developed a novel force clamp that operates without feedback, taking advantage of the anharmonic region of the trapping potential where the differential stiffness vanishes. We demonstrate the utility of such a force clamp by measuring the unfolding of DNA hairpins and the effect of trap stiffness on opening distance and transition rates.     

Apparent spin polarization decay in Cu-dusted Co/Al2O3/Co tunnel junctions

Co/Al2O3/Co magnetic tunnel junctions with an interfacial Cu layer have been investigated with in situ growth characterization and ex situ magnetotransport measurements. Cu interlayers grown on Co give an approximately exponential decay of the tunneling magnetoresistance with xi approximately 0.26 nm while those grown on Al2O3 have a decay length of 0.70 nm. The difference in decay lengths can be explained by different growth morphologies, and in this way clarifies a present disagreement in the literature. For monolayer coverage of Cu, we show that the tunneling spin polarization is suppressed by at least a factor of 2 compared to Co and beyond approximately 5 ML it becomes vanishingly small.     

Integral formulas with distribution kernels for irreducible projections in L2 of a nilmanifold

Let N be a simply connected nilpotent Lie group and Γ a discrete uniform subgroup. The authors consider irreducible representations σ in the spectrum of the quasi-regular representation N × L²(Γ/N) → L²(Γ→) which are induced from normal maximal subordinate subgroups M ? N. The primary projection P_σ and all irreducible projections P ? P_σ are given by convolutions involving right Γ-invariant distributions D on Γ→, $\text{Pf(Γn) = D 1 f(Γn) = <D, n · f>}\text{all}\text{f ? C}{}^{\mathrm{\infty }}\text{(Γ/N)}$, where n · f(ζ) = f(ζ · n). Extending earlier work of Auslander and Brezin, and L. Richardson, the authors give explicit character formulas for the distributions, interpreting them as sums of characters on the torus T^κ = (Γ ∩ M) · [M, M]?M. By examining these structural formulas, they obtain fairly sharp estimates on the order of the distributions: if σ is associated with an orbit $\text{O}$ ? $\text{n}$¹ and if $\text{V}$ ? $\text{n}$¹ is the largest subspace which saturates θ in the sense that f ? $\text{O}$ ? f + $\text{V}$ ? $\text{O}$. As a corollary they obtain Richardson's criterion for a projection to map C⁰(Γ→) into itself. The authors also resolve a conjecture of Brezin, proving a Zero-One law which says, among other things, that if the primary projection P_σ maps C^r(Γ→) into C⁰(Γ→), so do all irreducible projections P ? P_σ. This proof is based on a classical lemma on the extent to which integral points on a polynomial graph in Rⁿ lie in the coset ring of Zⁿ (the finitely additive Boolean algebra generated by cosets of subgroups in Zⁿ). This lemma may be useful in other investigations of nilmanifolds.     

Noncontact ultrasound stimulated optical vibrometry study of coupled vibration of arterial tubes in fluids

Coupled vibration of arterial tubes is analyzed with the wave propagation approach and first-order shear deformation theory. Both the interior and exterior fluids are considered as compressible so that acoustic waves can be generated and propagated in the fluids. Results obtained using the theory have been evaluated against those available in the literature and the agreement has been found to be good. The theory can be used for future research on the vibration and acoustics of arterial walls. Vibration experiments were carried out on a silicone rubber tube in a water tank with a novel ultrasound stimulated optical vibrometry system. This system uses the radiation force of ultrasound to vibrate the tube at low frequency and records the resulting response by a laser vibrometer. Both the excitation and measurement are remote and noncontact. The silicone rubber tube was chosen because it has mechanical properties close to those of arteries. The fundamental frequency is well excited by the radiation force and measured with the laser. The measured fundamental frequency is in good agreement with the present theory.