## Materials and Methods  
### Design of a Wireless Carotid Wearable Ultrasound Doppler System  
Figure 1 shows the functional block diagram of the proposed wireless carotid neckband ultrasound Doppler system. As shown in Figure 1, the two single-element transducers for the left and right common carotid arteries are used to transmit and receive ultrasound waves, and then the received radio-frequency (RF) ultrasound signals are quantized in analog-to-digital conversion (A/D conversion). In the pre-processing step, the quantized RF data are first transmitted with low-voltage differential signaling (LVDS) protocol and then converted as parallel data in the serial-to-parallel conversion, and the multiplexing (MUX) is used for selecting one of the two single-element transducers. After serial-to-parallel conversion and multiplexing, the quantized ultrasound RF data undergo high-pass filtering before quadrature demodulation to remove DC components, i.e., DC rejection filtering. To extract complex baseband data (i.e., in-phase and quadrature components), quadrature demodulation is performed, which involves multiplying the DC-rejected RF data by a carrier-frequency reference signal and then low-pass filtering the result of the multiplication [25]. After quadrature demodulation, complex baseband data are accumulated over the depth within a sample volume by using a window function (e.g., hanning). Lastly, wall filtering is applied to remove the clutter originating from slowly moving vessel walls and/or tissue movement [26]. After wall filtering, complex-based band data are transferred to an external smartphone for post-processing via Bluetooth 2.0. In the post-processing step, short-time fast Fourier transform (ST-FFT) is applied for generating Doppler spectra representing the changing velocity throughout the cardiac cycle and the distribution of velocities in the common carotid arteries [27; 28]. Then, the amplitude of the Doppler spectra is computed, and a thresholding operation is performed to remove the noise. The amplitude of the Doppler spectra undergoes compression, in which a predesigned nonlinear curve (e.g., log) is applied to adjust its dynamic range for enhanced visualization. Finally, a spectral Doppler waveform is generated, and some quantitative measurements are obtained (e.g., _PSV_ and _RI_). Figure 2 shows the overall system design of the proposed wireless carotid wearable ultrasound Doppler device supporting the functional blocks described in Figure 1. As shown in Figure 2, two 2.5-MHz single-element transducers are connected to a multi-channel pulser chip with a transmit/receive switch, and the received signals are sent to a multi-channel ultrasound analog front-end (AFE) chip consisting of low-noise amplifiers (LNAs), time-gain compensators (TGCs), programmable-gain amplifiers (PGAs), and 14-bit ADCs running at 40 MHz with a LVDS protocol. Figure 1: Functional block diagram of the wireless carotid wearable ultrasound Doppler system; ST-FFT: Short-time fast Fourier transform; PRF: Pulse-repetition frequency. Figure 2: Overall system design of the wireless carotid wearable ultrasound Doppler device; LNA: Low-noise amplifier; TGC: Time-gain compensator; PGA: Programmable gain amplifier; ADC: Analog-to-digital converter; RTC: Real-time controller; MUX: Multiplexer. An FPGA chip (Sparatan-6 LX150, Xilinx Inc., San Jose, CA, USA) is used for generating electrical pulses and is controlled by a real-time controller (RTC) based on the required PRF, and the chip is also used for performing pre-processing operations on the quantized ultrasound RF data. For pre-processing, a 128-tap finite impulse response (FIR) filter is employed to remove DC components in DC rejection filtering, and a direct digital synthesizer, mixer and digital filter are implemented for quadrature demodulation.