Turbulence quantification using high-frame-rate DUS

Future work will be directed towards the quantification of turbulence using the clinical modality of DUS. As discussed earlier, ultrasound offers a cost-effective and non- invasive diagnostic tool and is currently used for front-line examination before patients go through more elaborate and costly methods, such as MRI. TI has previously been quantified employing a conventional DUS system based on ensemble averaging of the mean velocity derived from spectral DUS [3-5], similar to the PIV ensemble-averaging method described in Chapter 4. Since only a single velocity measurement in the assigned sample volume is possible with DUS, the FOV was raster scanned to build TI maps in the above DUS studies. Comparison between the DUS and PIV TI maps of matched models shows qualitative agreement, and similarly eccentric plaques were found to be associated with higher amounts of turbulence. However, in DUS only the magnitude velocity in the direction of the transducer is captured thus contributing to an underestimation in TI compared to stereo-PIV, which provides all three components of the velocity.

Although the ensemble-averaging and raster-scanning methods can readily be applied to in vitro DUS studies, in clinical situations they can prove to be cumbersome owing to the considerably long acquisition time for multiple cardiac cycles or raster scanning and the need for cardiac (i.e. ECG) gating for phase synchronization, which are not part of a typical clinical protocol.

To circumvent these limitations, an alternative ultrasound method is sought that can provide full-field velocity maps thus eliminating the raster-scanning requirement. As discussed earlier, a new class of ultrafast ultrasound enables full-field acquisition of velocity maps with up to two in-plane components with frame rates in the order of kilohertz. We propose employing high-frame-rate color Doppler imaging methods, such as shown by Yiu and Yu [6] in a carotid artery with 25% stenosis. In their described method, three new additions (as opposed to conventional color Doppler) will result in significant improvement in the number of frame per second: plane-wave transmission, parallel receiving of pre-beamformed (raw) data from all channels, and parallel

beamforming. Our experiments are at preliminary stage and will be carried out in a recently fabricated vertical carotid artery model with 50% stenosis. A SonixRP ultrasound system will be used and is equipped with a multi-channel data acquisition module (SonixDAQ) that enables parallel acquisition (128 channels) of pre-beamformed data [7]. Plane waves will be transmitted with maximum pulse repetition frequency (PRF) of 10 kHz. Post-processing steps will be carried out in MATLAB-based programs. To achieve a high-resolution image, angular compounding of multiple (e.g. five) frames will be used yielding a lesser frame rate (e.g. 2 kHz) than the original PRF. Once the color maps are generated for multiple cardiac cycles, TI maps can be generated and compared to PIV measurements. Current limitations of this method, beside the single- component velocity measurements as mentioned above, is to incorporate ECG gating and also improve the signal-to-noise ratio by perhaps modifying the applied band-pass filter.

The implementation of POD-based turbulence quantification, as described in Chapter 3, overcomes the ECG-gating requirement. Moreover, our proposed POD-based turbulence quantification only requires a single cardiac acquisition. Two metrics – (1) exponential slope of inertial sub-range (i.e. intermediate modes) of the energy spectrum and (2) global entropy value – were demonstrated for quantifying turbulence. In order to obtain an approximate assessment of the effect of single-component velocity on the shape of the energy spectrum, a fractional energy spectrum derived from original 2D-3C velocity maps in a 70% concentric model is compared to a DUS-simulated energy spectrum as shown in Figure 6.1. The DUS-simulated velocity maps were obtained from original PIV velocity maps by only including the magnitude of the in-plane velocity component in the direction of an assumed Doppler angle of 65º (i.e. with the transducer lying in the x-y plane and a 65º steering angle relative to the x axis).

Figure 6.1a shows a comparison of the described energy spectra acquired with a 500-Hz frame rate. Compared to the first energy mode of the PIV spectrum (~72% of energy), the first mode in the DUS-simulated energy spectrum contains higher energy (82%) indicating that less of the turbulent energy is captured in the DUS-simulated velocity maps. However, comparison of the inertial sub-range shows close proximity between the two energy spectra resulting in similar decay slopes. In the DUS-simulated spectrum,

faster dissipation is observed, which compensates for the higher first-mode energy, thus conserving the total energy under the spectrum and making it equal to that of PIV. The faster dissipation in the DUS-simulated spectrum can be attributed to the lack of an out- of-plane component resulting in less sustention of turbulent energy.

Also, similar to the observation in the PIV-based POD energy spectrum in Chapter 3, lower temporal resolution does not result in notable change in the slope of the energy decay in the inertial range, as shown in Figure 6.1b for 100 and 500-Hz DUS-simulated spectra. A first mode energy of about 82% was captured in both cases. A larger velocity grid spacing of 0.6 mm – as typical of conventional DUS – resulted in a higher energy of the first mode (~85%); however, the overall shape of the energy spectrum was preserved by the lower energy levels in the remaining modes.

Future work will assess the possibility of POD-based turbulence quantification using high-frame-rate color Doppler ultrasound and validation with PIV measurements. Similar geometries of carotid artery models will be employed allowing direct comparison with our previous studies. It is expected that POD-based turbulence quantification could be further facilitated if ECG-gating was available, in which case only the portion of the cardiac cycle associated with the highest level of turbulence could be acquired for POD assessment as proposed by Grinberg et al. [8]. In this case, only the window containing the systolic deceleration phase of the cardiac cycle would need to be analyzed.