Application of Volterra Series to the Detection of Ultrasound Contrast Agents

Martin Schiffner, Michal Mleczko, Georg Schmitz

Proc IFMBE, 2009, Vol. 25, No. 2, pp. 478 - 481, DOI: 10.1007/978-3-642-03879-2_134


Ultrasound contrast agents (UCA) consist of microbubbles with mean diameters in the micron range. In ultrasound fields, these bubbles oscillate nonlinearly. Moreover, the nonlinearity of sound propagation in tissue cannot be ignored. Current strategies for UCA detection are designed by employing simple mathematical models, e.g. nonlinear characteristic curves or black box operators. Sophisticated physical models based on differential equations are often neglected due to their complexity. This contribution suggests the application of Volterra series as a well-interpretable, manageable tool with sufficient accuracy in the design and optimization of UCA detection strategies. A Volterra series describing nonlinear, dissipative plane wave propagation outside thermoviscous boundary layers according to the Burgers equation is derived and validated. It is employed to demonstrate possible optimizations in pulse subtraction imaging [1].


tags: Burgers equation, nonlinear acoustics, nonlinear sound propagation, nonlinear system theory, ultrasound contrast agents, Volterra