Spring-damper equivalents of the fractional, poroelastic, and poroviscoelastic models for elastography

In MR elastography it is common to use an elastic model for the tissue's response in order to properly interpret the results. More complex models such as viscoelastic, fractional viscoelastic, poroelastic, or poroviscoelastic ones are also used. These models appear at first sight to be very different, but here it is shown that they all may be expressed in terms of elementary viscoelastic models. For a medium expressed with fractional models, many elementary spring-damper combinations are added, each of them weighted according to a long-tailed distribution, hinting at a fractional distribution of time constants or relaxation frequencies. This may open up for a more physical interpretation of the fractional models. The shear wave component of the poroelastic model is shown to be modeled exactly by a three-component Zener model. The extended poroviscoelastic model is found to be equivalent to what is called a non-standard four-parameter model. Accordingly, the large number of parameters in the porous models can be reduced to the same number as in their viscoelastic equivalents. As long as the individual displacements from the solid and fluid parts cannot be measured individually the main use of the poro(visco)elastic models is therefore as a physics based method for determining parameters in a viscoelastic model.Comment: 11 pages, 7 figures. Changed inconsistent notation in Eqs 1, 5, 8, 10 and corrected mistakes in Eqs 2, 4, 12, 3

Real-time 3D medical ultrasound : signal processing challenges

Real-time 2D ultrasound systems are used routinely in every hospital and are a huge success both technically and commercially. This paper discusses the signal processing problems that needs to be tackled in order to move from 2D to 3D real-time ultrasound systems. The first problem discussed is that of handling 2000 10000 elements in the transducer. Sparse array methods is a way to reduce the number of elements and cost without compromising quality. Examples of performance with sparse arrays are presented. The second important problem is that of frame-rate. In 3D the frame-rate will be so low that real-time acquisition will be impossible unless some form of parallelism is exploited. Various ways of doing that such as multiple receive beams, coded transmit excitation and limited diffraction beams are discussed

Digital beamforming in ultrasound imaging

In medical ultrasound imaging, beam control methods such as dynamic focusing, and dynamic aperture and weighting give a need for more flexible control over the receive beam. In addition the desire to increase acquired framerate makes it a requirement to be able to receive several beams in parallel for each transmitted beam. Digital beamforming implemented with custom VLSI chips will give these capabilities. This paper therefore discusses various concepts for digital beamforming and also gives a discussion of the effect of time delay quantization in beamforming under conditions of steering and focusing