Modeling and phantom studies of ultrasonic wall shear rate measurements using coded pulse excitation

Wall shear rate (WSR) is the derivative of blood velocity with respect to vessel radius at the endothelial cell (EC) surface. The product of WSR and blood viscosity is the wall shear stress (WSS) that has been identified as an important factor for atherosclerosis development. High echo signal-to-noise ratio (eSNR) and high spatial resolution are crucial for minimizing the errors in WSR estimates. By transmitting coded pulses with time-bandwidth product greater than one, high eSNR from weak blood scatter can be achieved without increasing instantaneous power or sacrificing spatial resolution. This paper summarizes a series of measurements in a straight tube (5-mm diameter), constant velocity flow phantom using a 10 MHz transducer (60% bandwidth, f/1.5) imaged with a 72 degrees Doppler angle, 125 MHz sampling frequency and 1 kHz pulse repetition frequency. Measurements were made using a frequency-modulated (FM) code, phase-modulated (PM) codes, and uncoded broadband and narrow band pulse transmissions. Both simulation and experimental results show that coded-pulse excitation increases accuracy and precision in WSR estimation for laminar flow over a broad range of peak velocity values when compared to standard pulsing techniques in noise-limited conditions (eSNR < 30 dB). The code sequence and its length are selected to balance range lobe suppression with eSNR and echo coherence enhancements to minimize WSR errors. In our study, the combination of an eight bit Optimal coded pulse with a Wiener compression filter yielded the highest WSR estimation performance.