Ultrasound contrast imaging has been introduced in order to increase the contrast of echographic images by injecting micro-bubbles in the vascular system. They are gaz filled microbubbles with nonlinear behavior. One of the most used modality of ultrasound contrast imaging is the second harmonic imaging. This imaging technique, based on the reception of the second harmonic, is devoted to image only the nonlinearity of the microbubble. However, in such ultrasound images the contrast is limited by the nonlinear components of non-perfused tissue. Sub and ultra harmonic imaging appeared to be an interesting alternative to overcome this limitation since, unlike tissue, microbubbles generate sub and ultra harmonics. In order to extract optimally these sub and ultra harmonic components, we proposed a modified Hammerstein model able to model and extract sub and ultra harmonics. Results showed i) that microbubble signal is accurately represented both in time and frequency domains and ii) that sub-and ultra-harmonics were well extracted and separated from harmonic component. Note that the gain achieved by comparing the filtering signals by the modified Hammerstein and the standard Hammerstein was 4.6 dB.

Sub- and ultraharmonic (SUH) ultrasound contrast imaging is an alternative modality to the second harmonic imaging, since, in specific conditions it could produce high quality echographic images. This modality enables the contrast enhancement of echographic images by using SUH present in the contrast agent response but absent from the nonperfused tissue. For a better access to the components generated by the ultrasound contrast agents, nonlinear techniques based on Hammerstein model are preferred. As the major limitation of Hammerstein model is its capacity of modeling harmonic components only, in this work we propose two methods allowing to model SUH. These new methods use several Hammerstein models to identify contrast agent signals having SUH components and to separate these components from harmonic components. The application of the proposed methods for modeling simulated contrast agent signals shows their efficiency in modeling these signals and in separating SUH components. The achieved gain with respect to the standard Hammerstein model was 26.8 dB and 22.8 dB for the two proposed methods, respectively.

Sub- and ultraharmonics generation by ultrasound contrast agents makes possible sub- and ultraharmonics imaging to enhance the contrast of ultrasound images and overcome the limitations of harmonic imaging. In order to separate different frequency components of ultrasound contrast agents signals, nonlinear models like single-input single-output (SISO) Volterra model are used. One important limitation of this model is its incapacity to model sub- and ultraharmonic components. Many attempts are made to model sub- and ultraharmonics using Volterra model. It led to the design of mutiple-input singe-output (MISO) Volterra model instead of SISO Volterra model. The key idea of MISO modeling was to decompose the input signal of the nonlinear system into periodic subsignals at the subharmonic frequency. In this paper, sub- and ultraharmonics modeling with MISO Volterra model is presented in a general framework that details and explains the required conditions to optimally model sub- and ultraharmonics. A new decomposition of the input signal in periodic orthogonal basis functions is presented. Results of application of different MISO Volterra methods to model simulated ultrasound contrast agents signals show its efficiency in sub- and ultraharmonics imaging.

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