Variational approach for Stokes flow through a two-dimensional non-uniform channel.

A variational approach is proposed to study the Stokes flow in a two-dimensional non-uniform channel. By using the stationarity of the Lagrangian, the Euler-Lagrange equations are established which leads to a simple set of ordinary differential equations to provide an estimate for the average pressure drop explicitly in terms of the channel shape function. The results for the pressure drop show an excellent agreement with the second-order extended lubrication theory. A higher-order formulation further improves the accuracy of the results for the pressure drop along the channel.

Ultrasonic speed of sound dispersion imaging.

The feasibility for speed of sound dispersion (SOSD) imaging was investigated here. A through transmission new method for measuring the SOSD was utilized. With this method a long pulse comprising of two frequencies one being the double of the other is transmitted through the object and detected on its other side. SOSD projection images were obtained by scanning objects immersed in water using a raster mode utilizing a computerized scanning system. Using this approach SOSD projection images were obtained for solids and fluids as well as for a tissue mimicking breast phantom and an in vitro soft tissues phantom. The results obtained here, have clearly demonstrated the feasibility of SOSD projection imaging. SOSD may serve as a new contrast source and potentially may aid in breast diagnosis.

Measurement of speed of sound dispersion in soft tissues using a double frequency continuous wave method.

We introduce a method for measuring the speed of sound dispersion. It combines a short pulse transmission followed by a long burst comprised of two frequencies, one being double that of the other. The method allows the determination of the speed of sound dispersion using a single transmission. To validate the method, the dispersion was first measured in plastic samples and then in in vitro soft tissues samples. The results obtained for Perspex samples are in excellent agreement with values reported in the literature. The dispersion index in soft tissues ranged for a bovine heart from 0.63 +/- 0.24 (m/s.MHz) at 1.5 MHz to 0.27 +/- 0.05 (m/s.MHz) at 4.5 MHz and for a turkey breast from 1.3 +/- 0.28 (m/s.MHz) at 1.75 MHz to 0.73 +/- 0.1 (m/s.MHz) at 3.8 MHz. The significant difference in the speed of sound dispersion index between the studied materials indicates that dispersion may be used as a new index for soft tissue characterization by ultrasound.