Nonlinear modeling of ultrasonic transmit-receive system using Laguerre-Volterra networks

The precise knowledge of the electromechanical properties of an ultrasonic transmit-receive system can be used to optimize the excitation waveform in transmission-mode tomographic imaging. Although a linear system hypothesis is often postulated to model the dynamic transformation of the excitation waveform delivered at the transducer of the transmitter (input) into the received waveform at the receiver (output), linearity may not be appropriate in order to account for the actual dynamic characteristics of the system. In this work, we use a nonlinear system modeling/identification method to find a mathematical model of the nonlinear dynamic transformation between the excitation and received signals. The method employs the Laguerre-Volterra Network that has been successfully applied to modeling dynamic physiological systems. The obtained nonlinear model can be used to derive an optimal excitation waveform that produces the maximum peak value of the received signal for given power of the excitation signal. Using experimental data from a commercial ultrasonic array, we show how an optimal excitation signal can be derived from the obtained nonlinear model that maximizes the peak received value. We also demonstrate that the optimally designed excitation waveform offers significant performance improvement over conventional pulse waveforms (~35 times greater peak value).