## 2 Materials and Methods
### Automatic Range-Gate-Tracking Scheme in FPGA  
In the spectral Doppler mode of ultrasound, multiple ensemble signals from a single scanline are repetitively acquired to extract sample volumes from a range gate [23]. As mentioned before, this work uses a single-element transducer, so it acquires multiple ensemble signals from a single scanline to support a spectral Doppler mode. To automatically allocate a range gate on a scanline, we utilize the difference between adjacent ensemble signals to detect Doppler amplitude deviation, as illustrated in Figure 5. As is well known, ensemble signals from stationary tissue have almost the same phase and amplitude, because the same acoustic scattering of ultrasound is repeated. On the other hand, echo signals of ensembles have different phases along with amplitudes if echo occurs from moving particles or fluidic parts. Hence, the absolute difference between adjacent ensembles can result in Doppler amplitude deviation. In the conceptual illustration of Figure 5, the Doppler amplitude deviation results in relatively large amplitudes compared to other echo signal parts. Since we need to specify the estimated vessel position, we can use a slicing operation to indicate the position of the vessel. This slicing operation can be performed with a digital comparator circuit. The concept of tracking the position of a blood vessel, shown in Figure 5, utilizes Doppler amplitude deviation. However, the amount of Doppler amplitude deviation can be too small to apply the slicing operation, since the strength of scattering from the fluidic part is relatively small compared to the strength of scattering due to the acoustic impedance difference. Therefore, we need to amplify the Doppler amplitude deviation, which corresponds to the absolute value of difference between two adjacent ensemble echo signals. Figure 4: Timing diagram of high-voltage TX pulser; TX: transmitter, RX: receiver, MUX: multiplexer, HV: high voltage, ADC: analog-to-digital converter. This work utilizes an accumulation operation to enlarge the Doppler amplitude deviation of adjacent ensemble signals. Then, the enlarged Doppler amplitude deviation can make the slicing operation robust and consistent. Figure 6 illustrates a timing diagram of the automatic range-gate-positioning scheme based on the aforementioned accumulation of Doppler amplitude deviations. When a transducer is properly positioned on an arbitrary surface, the circuit system is triggered to track a vessel position on a scanline by using external switch toggling. Then, the circuit system starts to accumulate the absolute difference of adjacent ensembles, as shown in Figure 6. Through the successive accumulation operation, the Doppler amplitude deviation is amplified. Of course, the uncorrelated noise superimposed in the ensemble is also accumulated. This results in the elevation of the baseline of the accumulated ensemble difference, as shown in Figure 6. Since the variance of uncorrelated noise of ensembles is hard pre-estimate, the final elevated noise floor needs to be removed properly for a robust slicing operation. We apply a band-pass filter (BPF) to remove the noise floor (i.e., DC component) of the accumulated ensemble difference. The output of the band-pass filter is delivered to a hysteresis comparator to enable the range-gate indication signal _Range gate_, as shown in Figure 6. By using the enabled _Range gate_ signal, we can acquire a focal-point value, denoted as \(k\) in Figure 6. This focal-point value corresponds to an estimated position of a vessel on a scanline and is used to sort out the Doppler sample volumes. The proposed automatic range-gate-positioning scheme is implemented in the FPGA using the block diagram shown in Figure 7. It consists of BPFs, a de-multiplexer, first-in first-out (FIFO) memories, adders, and a hysteresis comparator. The output of the ADC is applied into _BPF1_, as shown in Figure 7. The filter _BPF1_ has the topology of a 4 th-order Butterworth filter, and its pass-band ranges from 1 MHz to 3 MHz.