Fig. 3

Reconstructed flow waveforms for the phantom experiment. a Pre-designed flow waveform (I) and reconstructed flow waveforms from the cine imaging method (b) and the proposed real-time imaging method (c). d Pre-designed flow waveform (II) and reconstructed flow waveforms from the cine imaging method (e) and the proposed real-time imaging method (f). Note that we manually repeated the cine flow waveforms in (b) and (e) with the gray color, which should facilitate the comparison with the proposed real-time imaging method. Here the flow waveforms from both the cine method and the real-time imaging method exhibit some discrepancy with the input waveform for the programmable pump during the periods of constant flow. This may be caused by the reflected bell-shape flow after it hits the wall of the tube