No abstract

A nonlinear system with third order nonlinearity is fully characterized using Symmetry Analysis applied to the excitation, as it is done in second order nonlinear systems using the pulse inverted method. Symmetry Analysis is performed using irreductible representations and the character table of C 3 rotation point group, which leads to the construction of three eigen-excitations allowing extraction of the third order nonlinearity parameter without the perturbation of fundamental and second order terms. Validation of this concept is based on Excitation Symmetry Analysis Method (ESAM) which was tested on simulated noisy signals and compared with classical spectral analysis.

Previous studies [R. Libgot, F. Ossant, Y. Gruel, P. Lermusiaux, and F. Patat, Proc.-IEEE Utrason. Symp. 4, 2259-2262 (2005); R. Libgot-Calle, F. Ossant, Y. Gruel, P. Lermusiaux, and F. Patat, Ultrasound Med. Biol. 34, 252-264 (2008); F. Ossant, R. Libgot, P. Coupe, P. Lermusiaux, and F. Patat, Proc.-IEEE Ultrason. Symp. 2, 846-849 (2004)] showed the potential of an in vitro high frequency ultrasound (beyond 20 MHz) device to describe the blood clotting process. The parameters were simultaneously estimated in double transmission (DT) with the calculation of the velocity of longitudinal waves and in backscattering (BS) modes with the estimation of the integrated BS coefficient and the effective scatterer size. The aim of the present study was to show how the integrated attenuation coefficient (IAC) assessed in DT mode could provide additional information on this process, especially regarding the fibrin polymerization which is an important part of the coagulation process. A characteristic time t(a) of the variations in IAC that could be linked to fibrin formation was identified.