Flow phantom

A dedicated flow phantom was used to perform the experiment. A tissue-mimicking gelatin phantom (as reported in ref. 20) containing a cylindrical cavity with a 6-mm diameter was employed. A solenoid pump E410 (CEME) was used to generate the flow. A calibrated flow value equal to 0.26 L/s was employed. A fixed volume (5 mL) of SonoVue® contrast agent with a concentration equal to 240 μL/L was repeatedly injected (manually) throughout the cavity. The cavity lay at a depth of 5 cm from the location of the probe and perpendicular to the imaging plane. Further down, at 8 cm, a PVC plate was positioned. The echoes which backscattered from the plate could therefore be recorded by the probe and used to form a tomographic image. At the same time, it was possible to measure the backscattered echoes from the microbubbles and use them to form harmonic images in echo graphic mode. This approach allowed us to compare the two imaging techniques, CPDI and HI, when (simultaneously) imaging the same bolus passage.

Data collection

An active sub-aperture of 64 elements was used to transmit and receive the ultrasound fields and linearly shifted over the 192-elements linear array to form a 128-line data set. The field of view was 20 mm wide and 90 mm deep. No focusing was applied in transmission and dynamic receive beamforming was used.

The post beam formed data were stored and used for the analysis. A 10-cycle pulse with its centre frequency at 2.5 MHz and whose amplitude was modulated by a Hamming envelope, was used as a driving signal. In receive mode, a sampling frequency of 50 MHz was used. A total of 80 frames were consecutively acquired for each bolus, at a frame rate of 8 Hz. A mechanical index (MI) equal to 0.07, which was measured with a hydrophone (HGL-0400 Onda, Sunnyvale, CA) at a depth of 5 cm, was used to minimize bubble disruption. The hydrophone, with a bandwidth ranging from 250 kHz to 20 MHz, was connected to a preamplifier (AH-2010-025 Onda, Sunnyvale, CA) whose bandwidth ranged from 50 kHz to 25 MHz, which in turn was connected to a 100 MHz A/D converter (PCI-5406 National Instruments, Austin, TX). Dedicated Labview® software was implemented and used for data acquisition. The MI was calculated as the ratio of the peak negative pressure in MPa and the square root of the frequency in MHz.

Data analysis

All data processing and analysis was performed using Matlab® R2014a.

Harmonic Imaging

The second harmonic (2H) component was extracted by band-pass filtering. A −12 dB bandwidth around 5 MHz was selected. Subsequently, a two-dimensional spatial Gaussian filter (spatial standard deviation σ x = 0.5 mm and σ z = 0.25 mm) was applied to enhance the signal-to-noise ratio. To reconstruct the harmonic images, an average speed of sound equal to 1510 m/s was assumed.

Cumulative Phase Delay Imaging

In order to measure the cumulative phase delay (CPD) between F0 and 2H, firstly, the pressure fields which had backscattered from the plate were selected by time-windowing (window length equal to 5 μs). Secondly, the two components, i.e., F0 and 2H, were extracted from the data (a −12 dB bandwidth was selected around 2.5 MHz and 5 MHz, respectively) and the corresponding envelopes were obtained by using the Hilbert transform. Thirdly, the time delay between the maxima of the fundamental and second harmonic envelopes was obtained for each line, providing a measure of CPD as a function of the lateral direction, i.e., a projection. For this experiment, the symmetry of the target was exploited for the reconstruction, in other words, CPD projections were assumed to be independent on the imaging angle. Finally, the filtered back-projection (filter type: Shepp-Logan) algorithm29 was used to generate 2D-CPD images.

Time Intensity Curve

To obtain the time intensity curves from the HI and CPDI data, the image intensity values were averaged over the region corresponding to the location of the cavity. Following that, a moving average filter (window size equal to 0.75 s) was applied and the baseline removed from the CPDI and HI TICs. The baseline was calculated as the mean value over the first 0.75 s. The average CPDI baseline was equal to −0.6 cycles/m.

Quantitative analysis

The peak time (PT) was calculated as the time when the maximum of a TIC was observed. The arrival time (AT) was estimated as the first time the TIC amplitude exceeded 5% of its value at PT. The wash-in time (WIT) was calculated as the time between AT and PT. The full width half maximum (FWHM) was calculated as the time interval over which the TIC amplitude stayed above 50% of its value at PT. The interval corresponding to the bolus passage is defined as the time between AT and the time showing a drop in TIC-amplitude below 5% of the value at PT. The area under the curve was derived as the sum of the TIC-amplitude values over the entire time window (10 s long) multiplied by the length of the sampling interval (0.125 s).

Speed-of-sound and attenuation estimation

By using the same filtered back-projection algorithm that was applied to perform CPDI, tomographic images based on speed-of-sound and attenuation were obtained from the variations in the time-of-flight and amplitude of the peak of the fundamental envelope, respectively. Subsequently, histograms were obtained by analysing the image values over the region corresponding to the location of the cavity, during the passage of the boluses.

Dispersion evaluation

Values of CPD in tissue are determined by the combined effect of tissue nonlinearity and frequency dispersion20. Both phenomena result in a negative CPD value. However, the contribution due to tissue nonlinearity can be assumed to be negligible as compared to that due to frequency dispersion, especially for highly absorbing tissues. In fact, in line with the Kramers-Kronig relationship30, dispersion and absorption are interlinked. In conclusion, to evaluate CPD values, absorption measures reported in ref. 26 for blood, fat and breast tissue were used in combination with the theoretical model in ref. 25.