Continuous non-equilibrium transition driven by the heat flow

We discovered an out-of-equilibrium transition in the ideal gas between two walls, divided by an inner, adiabatic, movable wall. The system is driven out-of-equilibrium by supplying energy directly into the volume of the gas. At critical heat flux, we have found a continuous transition to the state with a low-density, hot gas on one side of the movable wall and a dense, cold gas on the other side. Molecular dynamic simulations of the soft-sphere fluid confirm the existence of the transition in the interacting system. We introduce a stationary state Helmholtz-like function whose minimum determines the stable positions of the internal wall. This transition can be used as a paradigm of transitions in stationary states and the Helmholtz-like function as a paradigm of the thermodynamic description of these states

Statistical properties of pulse-echo signal backscattered in trabecular bone

The paper considers the application of statistical properties of backscattered ultrasonic signal for assessment of the trabecular bone status. Computer simulations were conducted to investigate the properties of the ultrasound pulse-echo signal, as it is received on the transducer surface after scattering in trabecular bone. Results indicated that while for the well-defined trabeculae properties within the simulated bone structure the signal envelope values are Rayleigh distributed the significant departures from Rayleigh statistics may be expected as the thickness of trabeculae become random. The influence of the altering of mechanical properties of the bone tissue building the trabeculae on the signal statistical parameters was unnoticeable. The initial experiments confirming some cases of departure from Rayleigh statistics for envelopes of backscattered signals are also discussed

Statistics of Envelope of High-Frequency Ultrasonic Backscatter from Trabecular Bone: Simulation Study

The paper considers the application of statistical properties of backscattered ultrasonic signal for assessment of the trabecular bone status. Computer simulations were conducted to investigate the properties of the ultrasound pulse-echo signal, as it is received on the transducer surface after scattering in trabecular bone. The micro-architecture of trabecular bone was modeled by a random distribution of long and thin cylindrical scatterers of randomly varying diameters and mechanical properties, oriented perpendicular to the ultrasound beam axis. The received echo signal was calculated as a superposition of echoes from all the scatterers present in the scattering volume. The simulated signal envelope was used for statistical processing to compute various parameters like the mean amplitude, the amplitude MSR defined as the ratio of the mean to the standard deviation and the amplitude histogram. Results indicated that while for the well-defined trabeculae properties within the simulated bone structure the signal envelope values are Rayleigh distributed the significant departures from Rayleigh statistics may be expected as the thickness of trabeculae become random. The influence of the variation of mechanical properties of the bone tissue building the trabeculae on the bone backscattered signal parameters was not observed

Parametric imaging of a trabecular bone by a Scanning Acoustic Microscope

A nondestructive method is proposed for bone quality assessment at a resolution of about 200 µm. The properties of the bone matrix itself, independent of the mass or porosity of the bone, can be determined using a Scanning Acoustic Microscope (SAM). The high resolution of the SAM makes it possible to image a single trabecula of the biopsed iliac bone sample. Two microscopic acoustic images of a trabecula are recorded. The first is created by the waves reflected from the surface of the sample. The other is formed by the reflections from the bottom. These images are processed further and two parametric images are calculated. They reflect the distribution of impedance and attenuation in the bone. The method is applied to examine trabeculae in bone samples biopsed from patients with metabolic bone diseases

Multiple scattering contribution to trabecular bone backscatter

Integral equations that describe scattering on the structure with step rise parameters, have been numerically solved on example of the trabecular bone model. The model consists of several hundred elements with randomly selected parameters. The spectral distribution of scatter coefficients in subsequent orders of scattering has been presented

Example of Structure Modeling and Analysis of Ultrasound Scattering for Trabecular Bone

A trabecular bone consists of trabeculae whose mechanical properties differ significantly from the surrounding marrow, therefore an ultrasonic wave propagating within the bone structure is strongly scattered. The aim of this paper was to evaluate the contribution of the first, second and higher order scattering (multiple scattering) into the total scattering of ultrasound in a trabecular bone. The scattering due to the interconnections between thick trabeculae, usually neglected in trabecular bone models, has been also studied. The basic element in our model of the trabecular bone was an elastic cylinder with a various finite-length and diameter as well as orientation. The applied model was taking into account variation of both, elements size and their spatial configuration. The field scattered on the bone model was evaluated by solving numerically the integral form of the generalized Sturm-Liouville equation describing a scalar wave in inhomogeneous and lossy media. For the scattered fields calculated numerically the effective cross-sections were determined. The influence of absorption on the scattering coefficients was demonstrated. The results allowed to conclude that within the frequency range from 0.5 to 1.5 MHz contribution of the second order scattering to the effective backscattering cross-section is at least 500 times lower than that due to the first order scattering. It was noticed that for a frequency higher than 1.5 MHz fast growth of the backscattering (reflection) coefficients, calculated for the second order scattering, occurs

Tissue Attenuation Estimation from Backscattered Ultrasound Using Spatial Compounding Technique - Preliminary Results

The pathological states of biological tissue are often resulted in attenuation changes. Thus, information about attenuating properties of tissue is valuable for the physician and could be useful in ultrasonic diagnosis. We are currently developing a technique for parametric imaging of attenuation and we intend to apply it for in vivo characterization of tissue. The attenuation estimation method based on the echoes mean frequency changes due to tissue attenuation dispersion, is presented. The Doppler IQ technique was adopted to estimate the mean frequency directly from the raw RF data. The Singular Spectrum Analysis technique was used for the extraction of mean frequency trends. These trends were converted into attenuation distribution and finally the parametric images were computed. In order to reduce variation of attenuation estimates the spatial compounding method was applied. Operation and accuracy of attenuation extracting procedure was verified by calculating the attenuation coefficient distribution using the data from the tissue phantom (DFS, Denmark) with uniform echogenicity while attenuation coefficient underwent variation

Synthetic Aperture Technique Applied to Tissue Attenuation Imaging

The attenuating properties of biological tissue are of great importance in ultrasonic medical imaging. Investigations performed in vitro and in vivo showed the cor- relation between pathological changes in the tissue and variation of the attenuation coefficient. In order to estimate the attenuation we have used the downshift of mean frequency (fm) of the interrogating ultrasonic pulse propagating in the medium. To determine the fm along the propagation path we have applied the fm estimator (I/Q algorithm adopted from the Doppler mean frequency estimation technique). The mean-frequency shift trend was calculated using Single Spectrum Analysis. Next, the trends were converted into attenuation coefficient distributions and finally the parametric images were computed. The RF data were collected in simulations and experiments applying the synthetic aperture (SA) transmit-receiving scheme. In measurements the ultrasonic scanner enabling a full control of the transmission and reception was used. The resolution and accuracy of the method was verified using tissue mimicking phantom with uniform echogenicity but varying attenuation coefficient

Theoretical results and numerical study on the nonlinear reflection and transmission of plane sound waves

The comparison between theoretical and numerical solutions of the reflection/transmission problem for the acoustic plane wave normally incident on the discontinuity surface between two nonlinear lossy media was presented. Numerical calculations made under the assumption that the two media have the same impedance, allow to single out the effect of nonlinearities in the description of the reflection and transmission phenomena, so they agreed with theoretical predictions. It was shown that theoretically obtained and numerically calculated results mutually confirmed themselves

Assesment of cortical bone thickness using cepstrum analysis. Simulation study

Assessment of cortical bone thickness is important from a medical point of view because bone-layer thickness has a diagnostic value. The thinning of the cortical bone layer reduces the mechanical strength of the bone and exposes it to an increased risk of osteoporotic fractures [1]. The hip bone (proximal femur) is the most critical fracture site. The thickness of the cortical layer in the proximal femur is often too thin to be detected from ultrasonic echoes using traditional peak detection methods (for example the envelope method). In such a case the cepstrum analysis technique may be very useful. In this study the cepstrum method was applied to analyze numerically simulated echoes reflected from the layer and to determine layer thickness. In simulation, the transducer operated at 1 MHz and pulses of a 1.5 µs duration were assumed. The thickness of the thinnest layer for which the applied cepstrum analysis gave, the correct result equaled 1 mm, which was ¼ ƛ(ƛ– wavelength of an ultrasonic wave). That value of the d/ƛ ratio is sufficient for future measurements performed in-vivo conditions