A discrete nonlinear system driven at one end by a periodic excitation of frequency above the upper band edge (the discreteness induced cutoff) is shown to be a means to (1) generate propagating breather excitations in a long chain and (2) reveal the bistable property of a short chain. After detailed numerical verifications, the bistability prediction is demonstrated experimentally on an electrical transmission line made of 18 inductance-capacitance (LC) cells. The numerical simulations of the LC -line model allow us also to verify the breather generation prediction with a striking accuracy.
This study aims at evaluating Magnetic Resonance Elastography (MRE) as a reliable technique for the characterization of viscoelastic properties of soft tissues. Three phantoms with different concentrations of plastisol and softener were prepared in order to mechanically mimic a broad panel of healthy and pathological soft tissues. Once placed in a MRI device, each sample was excited by a homemade external driver, inducing shear waves within the medium. The storage (G') and loss (G") moduli of each phantom were then reconstructed from MRE acquisitions over a frequency range from 300 to 1,000 Hz, by applying a 2D Helmholtz inversion algorithm. At the same time, mechanical tests were performed on four samples of each phantom with a High-Frequency piezo-Rheometer (HFR) over an overlapping frequency range (from 160 to 630 Hz) with the same test conditions (temperature, ageing). The comparison between both techniques shows a good agreement in the measurement of the storage and loss moduli, underlying the capability of MRE to noninvasively assess the complex shear modulus G* of a medium and its interest for investigating the viscoelastic properties of living tissues. Moreover, the phantoms with varying concentrations of plastisol used in this study show interesting rheological properties, which make them good candidates to simulate the broad variety of viscoelastic behaviors of healthy and pathological soft tissues.
Magnetic resonance elastography (MRE) is used to non-invasively quantify viscoelastic properties of tissues based on the measurement of propagation characteristics of shear waves. Because some of these viscoelastic parameters show a frequency dependence, multifrequency analysis allows us to measure the wave propagation dispersion, leading to a better characterization of tissue properties. Conventionally, motion encoding gradients (MEGs) oscillating at the same frequency as the mechanical excitation encode motion. Hence, multifrequency data is usually obtained by sequentially repeating monochromatic wave excitations experiments at different frequencies. The result is that the total acquisition time is multiplied by a factor corresponding to the number of repetitions of monofrequency experiments, which is a major limitation of multifrequency MRE. In order to make it more accessible, a novel single-shot harmonic wideband dual-frequency MRE method is proposed. Two superposed shear waves of different frequencies are simultaneously generated and propagate in a sample. Trapezoidal oscillating MEGs are used to encode mechanical vibrations having frequencies that are an odd multiple of the MEG frequency. The number of phase offsets is optimized to reduce the acquisition time. For this purpose, a sampling method not respecting the Shannon theorem is used to produce a controlled temporal aliasing that allows us to encode both frequencies without any additional examination time. Phantom experiments were run to compare conventional monofrequency MRE with the single-shot dual-frequency MRE method and showed excellent agreement between the reconstructed shear storage moduli G 0. In addition, dual-frequency MRE yielded an increased signal-to-noise ratio compared with conventional monofrequency MRE acquisitions when encoding the high frequency component. The novel proposed multifrequency MRE method could be applied to simultaneously acquire more than two frequency components, reducing examination time. Further studies are needed to confirm its applicability in preclinical and clinical models.
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