Study population

This single-center, prospective, observational study was conducted between November 2022 and March 2023. Ultrasound data and 4-D flow MRI scans were acquired in 20 healthy subjects (10 men; median age, 49 years; range, 24 to 75 years) without any history of cardiovascular or pulmonary disease or a contraindication for MRI. The study was performed in accordance with the World Medical Association Declaration of Helsinki. Informed consent was obtained from all participants. The study was approved by the authorized regional Medical Ethics Committee (NL80478.091.22) and the institutional review board, and registered at ClinicalTrials.gov (NCT05451485).

Ultrasound examination

All subjects underwent an ultrasound examination of the left carotid bifurcation when in supine position. US-VVI data were acquired at the carotid bifurcation, using an L12-5 50 mm transducer (Philips (ATL), Bothell, WA, USA) connected to a Verasonics Vantage 256 system (Verasonics, Kirkland, WA, USA). To facilitate proper transducer placement, real-time B-mode imaging was shown at 60 Hz, using eleven-angled coherently compounded plane waves between −10° and +10°. When the correct plane was imaged through the lumen center of the carotid bifurcation, a 3 second US-VVI acquisition was started. The US-VVI acquisition consisted of repeated −20° and +20° steered plane waves transmitted at a pulse repetition frequency of 10 kHz. Before saving the raw radiofrequency (RF) channel data, visual inspection of singular value decomposition-based clutter-filtered data served as quality check to confirm the presence of sufficient blood signal in the vessel lumen. The acoustic output of this imaging sequence was tested to be within the stated acoustic safety limits for peripheral vessel applications [ ], with a mechanical index of 0.56, I _sppa,3 of 46.9 W/cm ² , and I _spta,3 of 137 mW/cm ² . Regarding thermal safety, the high frame rate US-VVI acquisition duration is restricted to a maximum of 20 seconds. Therefore, the 3 second US-VVI acquisition does not exceed the maximum transducer contact surface temperature [ ]. An overview of the transducer and transmit parameters is provided in Table 1 . The active aperture of both plane waves was selected such that there was a maximum overlap of both steering beams at the center of the carotid artery. The US-VVI measurement was repeated three times, two times by a technical physician experienced with US-VVI measurements (observer 1) and once by an experienced sonographer (observer 2). Both examiners were blinded from each other’s ultrasound acquisitions.

US-VVI analysis

The stored RF channel data were processed offline using MATLAB (version R2023a; The MathWorks, Natick, MA, USA). A detailed description of each post-processing step is reported previously by Saris et al. (2019) [ ]. A delay-and-sum beamformer was used to reconstruct the angled acquisitions into RF image lines on a cartesian grid oriented along the steering direction with a resolution (axial × lateral) of 12.3 × 51.7 µm [ ]. To suppress static tissue signal without sacrificing frames for filter initialization, a 150th order temporal sliding high-pass finite impulse response filter with a short transition region (−80 dB − 0 dB, 1 cm/s) was applied. The cut-off value (at −55 dB) was dynamically adapted to be equal to the 90th percentile of the absolute vessel wall displacement within an ensemble. Interframe tracking of the vessel wall contour and blood speckle in the vessel lumen was performed using a two-iteration, normalized cross-correlation based algorithm [ ], which was applied to the angled acquisitions separately ( Table 2 ). The displacement, or velocity, between two frames was estimated via the peak in the correlation map. The 2-D velocity vector maps were obtained by using the displacement compounding approach [ ], in which compounding of both angled axial estimates was performed when the correlation peak value for both angles was above 0.4 for more than 15 estimates within an ensemble. When this condition was met by only one of the angles, projection of this single-angle estimate was performed. When both angles did not match this condition, compounding was used and the final velocity vector was marked unreliable. The median of 39 compounded or projected interframe estimate, that is, 8 ms, was used to obtain a single ensemble averaged velocity estimate, resulting in 125 velocity vector fields per second. These estimates where first spatially filtered, followed by temporal averaging of three consecutive ensemble estimates, using a weighting of [0.25, 0.5, 0.25]. The final grid size of the velocity vector fields was 0.1 × 0.1 mm ( Table 2 ).

4-D flow MRI

All subjects underwent a free-breathing and retrospective vectorcardiographic-gated RF-spoiled gradient echo MRI scan with 3-D velocity encoding of the left carotid bifurcation. Images were obtained using a 3.0T MRI system (Ingenia, Philips Healthcare, Best, the Netherlands) together with a 20 channel head-and-neck coil (dStream, Philips Healthcare). The orientation of the head resembled the position during the ultrasound examinations. An overview of all acquisition settings is provided in Table 3 . MRI examination took place within 1 week after the ultrasound examination. Aliasing artefacts were prevented by setting the velocity encoding sufficiently high based on the MRI flow scout measurement. MRI data were corrected for offset and aliasing using CAAS software (Pie Medical, Maastricht, the Netherlands).

Registration of US-VVI and 4-D flow MRI

Semiautomatic registration of the 2-D ultrasound and 3-D MRI magnitude data was performed at peak systole using an in-house build registration algorithm, to find the slice through the 3-D MRI volume that best matched the 2-D ultrasound image ( Fig. 1 ). The lumen of the carotid artery was manually annotated in the 2-D ultrasound image and masking was applied to generate a binary image. The 3-D MRI magnitude data were cropped (71 × 51 × 31 voxels) around the left carotid bifurcation. Thresholding of the cropped magnitude data was automatically performed using the triangle method [ , ], which generated a 3-D binary MRI segmentation of the vessel lumen. When necessary, the resulting segmentation was adjusted manually to exclude the jugular vein.

Visualization of the semiautomatic registration algorithm, to find the 2-D plane through the 3-D MRI volume that best matches the 2-D ultrasound image. The manual initialization was followed by three iterations of automated optimization, where translation (t _x , t _y , t _z ) and rotation (θ _x, θ _y, θ _z ) were performed in all three spatial directions to find the best match, that is, the lowest sum of absolute differences, between the 2-D MRI plane and the annotated ultrasound vessel lumen. MRI, magnetic resonance imaging; US, ultrasound.

The registration process consisted of a manual initialization followed by an automatic optimalisation. First, the user initialized a 2-D slice through the 3-D binary MRI segmentation which best matched the 2-D binary ultrasound image. The manual initialization was followed by a three-iteration automated optimization step, where stepwise translation and rotation was performed to optimize the 2-D MRI slice selection. The geometrical similarity between the binary ultrasound and MRI plane was assessed by the sum of absolute difference (SAD). Here, upsampling of the binary MRI plane (29 × 21), using nearest neighbor, was needed to match the size of the binary ultrasound image (2841 × 479). In the first iteration, translation and rotation in all three spatial directions were restricted to 5 mm (stepsize 2 mm) and 20° (stepsize 10°), respectively. The combination of translation and rotation resulting in the lowest SAD was defined as best match and used as input for the next iteration. In the final iteration, translation and rotation steps of 0.5 mm and 2° were used to select the best match between the binary MRI and ultrasound plane, and thus the optimal 2-D slice through the 3-D MRI volume. The 3-D MRI velocity vectors were projected on this 2-D slice and compared against the velocity vectors from US-VVI.

Comparison of US-VVI with 4-D flow MRI

All 60 ultrasound datasets were registered to the MRI data. Datasets with a relative SAD (SAD _rel ) of less than 20% were defined as trustworthy and used for further analysis, with SAD _rel defined as:

The full 2-D velocity vector fields of US-VVI and 4-D flow MRI in the registered plane were compared at peak systole and end diastole by calculating the average cosine similarity in the carotid bifurcation, that is, the cosine of the angle between the MRI- and ultrasound-based velocity vectors, and the root-mean-square error of the velocity magnitudes (RMSE _mag ) between the modalities. The US-VVI velocities were averaged spatially to match with the MRI resolution, that is, 1.2 × 1.2 mm in the axial and lateral directions. Only reliable US-VVI estimates were taken into account.

Furthermore, temporal velocity profiles were extracted from the 2-D velocity fields of both modalities in the common carotid artery (CCA) and internal carotid artery (ICA). The agreement between the temporal velocity profiles were compared by calculating the similarity according to:

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