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Computational and Mathematical Methods in Medicine
Volume 2013, Article ID 934538, 9 pages
Research Article

A General Framework for Modeling Sub- and Ultraharmonics of Ultrasound Contrast Agent Signals with MISO Volterra Series

1Université François Rabelais de Tours, UMR-S930, 37032 Tours, France
2INSERM U930, 37032 Tours, France
3IUT Ville d’Avray, Université Paris Ouest Nanterre La Défense, 92410 ville d’Avray, France
4Département de Physique et d’Électronique, Faculté des Sciences I, Université Libanaise, Hadath, Lebanon

Received 21 December 2012; Accepted 25 January 2013

Academic Editor: Kumar Durai

Copyright © 2013 Fatima Sbeity et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.