Can echocardiographic particle image velocimetry correctly detect motion patterns as they occur in blood inside heart chambers? A validation study using moving phantoms

In order to produce ultrasound images with a distinct speckle pattern with linear motion of known speed and direction, a commercially available high fidelity Doppler testing device (DP1, BBS Medical Electronic AB, Hägersten, Sweden) was used. It consisted of a loop of surgical silk tautened between two pulleys. The position of the pulleys could be adjusted in a way that the insonation angle at which the string was imaged could be changed between 0 and 90 degrees (Figure 1A) [8, 9]. A watertight DC-motor, controlled by an external control unit, drove one of the pulleys. The control unit allowed to set the rotational speed of the motor to a constant value or to program repetitive sequences of velocity profiles [8, 9]. A tachometer was directly attached to the motor shaft and allowed to measure the actual rotational speed with high fidelity. The tachometer signal was also available as a proportional analogue output which was fed into a physio-channel of the ultrasound system and digitally stored together with the image data. The speed of the string was calculated by multiplying the known circumference of the pulley with the rotational speed of the motor.

The rotating phantom was used to test both, the flow recognition at different angles as well as the vortex recognition algorithm. A flat cylinder of agar of 3 cm thickness and 10 cm in diameter was cast on a disc of acrylic glass. Holes were punched in the agar with a fine needle in a way that an evenly distributed pattern of distinct speckles was obtained when the phantom was imaged. The disc with the agar phantom was directly fitted to the shaft of the DC-motor of the same testing device [10] (Figure 1B). The tangential velocity of a certain point in the agar phantom could be calculated by multiplying its distance from the motor axis with 2π and the rotational speed of the motor.

Phantoms were submerged in a rubber damped tank which was filled with degassed tap water. The ultrasound transducers were placed in a tripod and positioned just below the water surface. A regular attenuator, as used to avoid near field artefact in soft tissue imaging, was placed under the probes (Figure 1A and 1B).

The string phantom could be turned to obtain different insonation angles. Care was taken to center the ultrasound transducer over the tilt axis of the string phantom which was then imaged at a depth of approximately 7.5 cm. Similarly, the rotating phantom was positioned in the center of the image with its rotational axis at a depth of approximately 9.5 cm.

Images were collected with high-end ultrasound systems (Siemens Acuson SC 2000, Siemens Medical Solutions, Mountain View, USA, probe: 4V1c-S, 1.0-4.0 MHz; GE Vivid E9, Vingmed Ultrasound, Horten Norway, probe: M3S, 1.5-4.0 MHz; Philips iE33, Philips Ultrasound, Bothell, WA, USA, probe: S5-1, 1.0-5.0 MHz). Image loops of at least three seconds were digitally stored at three different gain settings (−10, 0, +10 dB) to allow the selection of the optimal image for subsequent off-line analysis. The optimal image was selected, if already in part a pure visual tracking of specific speckle-patterns was possible.

In order to investigate the influence of frame rate, three different acquisition settings resulting in comparable frame rate ranges (38–44 fps, 56–62 fps and 74–81 fps) were used in all ultrasound machines.

To investigate the influence of axial vs. lateral resolution, the insonation angle of the string was changed between 15 and 90 degrees in steps of 15 degrees (Figure 2A). Similarly, measurements at different points of the rotating phantom also allowed to investigate changing insonation angles (Figure 2B).

For determining the accuracy of velocity and angle estimates, the rotating phantom was driven at different continuous speeds resulting in circumferential velocities between 5 and 400 cm/s.

In order to investigate the limits of tracking, both the string and the rotating phantom were driven using a ramp pattern with increasing string speed up to a varying plateau between 10 and 100 cm/s. The ramp was repeated 60 times per minute.

Echocardiographic image loops were processed offline using a dedicated prototype software (Omega Flow Version 2.3.1.). Since the software is designed for ventricular flow analysis, the first analysis step is to trace and track the endocardial border of the cavity of interest. For the string phantom image loops, we drew a virtual endocardial contour in ca. 2 cm distance to the string in the center of the image. In the rotating phantom image loops, the contour was just enveloping the phantom. In both, the endocardial tracking function of the program was switched off in order to keep the contour stable (Figure 3 A and D).

In a second step, the circumscribed area of interest is analyzed by the feature tracking algorithm of the program which provides a matrix of instantaneous local flow velocity vector estimates based on the tracking of the moving scatterers (Figure 3B and E). Generally, the highest possible matrix density setting was used (approx. one vector estimate per 8*8 image pixels). For evaluating the vortex recognition in images from different machines, medium and low matrix density settings were tested as well.

The velocity matrix is then used to calculate the local in-plane vorticity. The software provides an estimate of the position and size of the dominant clockwise and counterclockwise vortices within the circumscribed region. For the latter, the threshold for including detected vortical flow in the main vortex area could be set as 25%, 50%, 75% or 100% of the maximum heartbeat-averaged steady-streaming field (Figure 3C). We defined the biggest continuous area of vortical flow as steady-streaming field.

Both the velocity matrix as well as the vortex characteristics were exported for further analysis [4, 5].

For evaluation of the accuracy of the estimates of flow direction and velocity as well as for determining the maximally measurable flow velocity (cut-off velocity) we used a dedicated, custom made, MATLAB based software tool (dFlow, JUV, Catholic University Leuven) which allowed to extract curves of regional velocity and motion direction from each point of the velocity matrix and to compare those to the true velocity profiles which had been stored as synchronous physio-trace with the image data (see example in Figure 4A).

For string phantom data, the sample volume of the dFlow program was placed in the midline of the image sector directly on the string. In the rotating phantom clips, the sample volume was positioned in a way that different insonation angles could be investigated. The distance of the sample volume to the phantom center of rotation was measured in the image in order to scale the known velocity profile of the phantom to the true velocity in sample position (Figure 2 A and B).

When using a ramp profile exceeding the highest trackable velocity, velocity estimates of the PIV software followed the true velocity profile up to a certain point and showed then a random pattern (see example in Figure 5A). To determine this cut-off velocity in an objective way, a statistical approach was used: In a linear regression model with the true velocities on the x axis and the estimated velocities on the y axis, the fit of a linear regression line crossing the coordinate origin was calculated for a stepwise inclusion of data pairs of increasing true velocities. The true velocity at the step with the maximum fit served as cut-off velocity (see example in Figure 5B).

In the string phantom, velocity estimates from the center of the image were compared to the known velocity using the method of Bland and Altman [11]. In the rotating phantom, error histograms of the entire flow field were calculated. In ramp profiles, data below and above the cut-off velocity were considered separately.

In the string phantom, a direction estimate from the center of the image was analyzed. A deviation from the true angle of less than ± 10° was arbitrarily accepted as accurate and the relative frequency of accurate measurements was determined in relation to the true velocity of the phantom. In the rotating phantom, the deviation of the angle estimate from the truth was analyzed using error histograms for the entire flow field. In ramp profiles, data below and above the cut-off velocity were considered separately (see example in Figure 5 C and D).

In general, continuous variables are presented in the following as mean ± standard deviation (SD). Linear regression was used to investigate the relation between two parametric variables. Continuous measurements were compared by Spearman correlation and a Bland-Altman-Analysis. A two-tailed p value of < 0.05 was considered significant. Statistical analyses were performed with MATLAB (dito) and the PASW™ software (SPSS Inc., Chicago, Illinois).

Direction estimates proved to be less sensitive to changing acquisition settings. We found no significant relation between the frequency of accurate direction estimates and frame rate. However, we noticed a relation to the insonation angle. The error of the direction estimate was lowest when the motion was close to the beam direction (Figure 6C).

Estimates became already accurate at very low velocities (above 4–8 cm/s) and remained stable up to the cut-off-velocity. Above the cut-off-velocity, estimates were less, but still sufficiently accurate (see example in Figure 5C and 5D). Under optimal conditions (low insonation angle in string phantoms), direction estimates deviated less than ±10° from the true direction in 86.7 ± 1.5% of all frames.

The PIV software was able to identify the rotating agar phantom as vortex (see example in Figure 3C). The vortex center was accurately identified with a minor offset of < 5.5 mm. Interestingly, the size of the indicated vortex region varied with the rotational speed of the phantom. The identified vortex had at maximum an approximate diameter of 2/3 of the region of the phantom in which the tangential velocities were still below the cut-off velocity for tracking. In general, the accuracy of the detection of the vortex center (p = 0.5) and the estimation of vortex size (p = 0.4) did not depend on the density settings of the flow vector field.

The maximally detectable velocity (cut-off velocity) in the different high-end ultrasound machines was comparable (44 cm/s, 42 cm/s, and 42 cm/s, n.s.). We found further no significant differences for direction estimation in the different machines (80–90% of all frames within the ±10° range of the true direction for all machines).

The error for the vortex center detection was comparable (4.7 ± 3.5 mm, 5.5 ± 3 mm and 4.0 ± 3.1 mm). Acquisition and post-processing settings had no relevant impact on the accuracy of the vortex pattern recognition in image loops from the different machines.

We noted a counterclockwise vortex in the four-chamber-view of the LV during diastole in all patients (Figure 8A). In the LV three-chamber-view, a clockwise rotation of the blood was seen (Figure 8B). In the RV, minor diastolic vortices were noted just above the tricuspid valve (Figure 8C).

In concordance with the phantom experiments, the cut-off velocity proved to be linearly dependent on frame rate (r = 0.94, p < 0.01) (Figure 4C).

Surprisingly, flow direction estimates remained reasonably accurate even above the cut-off velocity (Figure 5C and 5D). We hypothesize that this phenomenon could be explained if the correlation of speckle patterns between frames is higher in the direction of flow than it is perpendicular to flow.

The displayed vortex size was dependent on the rotational speed of the phantom, but always smaller than the phantom size. While the former is explained by the loss of tracking in the outer regions of the phantom which exceed the cut-off velocity, the latter effect is due to the particularities of the rigid phantom. In contrast to a fluid vortex in the heart which has centrifugally decreasing angular velocities and therefore its highest vorticity in the center, the rigid phantom shows constant angular velocities in all parts which results in highest vorticity values at the outer edge. Under such circumstances, the implemented algorithm - which looks for a compact vorticity region above a certain threshold percentage of the heart beat averaged maximum vorticity – results in a radius of the displayed vortex (r_v) proportional to the phantom radius (R): r v ≈ R 2 * t h r e s h o l d (personal communication with G. Pedrizzetti, University of Trieste, Italy).

We observed no relevant difference between the tracking results from image loops acquired with the different high-end ultrasound machines. This may not fully reflect clinical reality since our phantoms, providing close-to-ideal imaging conditions, did not challenge the imaging capabilities of the different systems. Our results show clearly, however, that care must be taken to preserve original image resolution and frame rate during DICOM-conversion.

Our findings indicate that requirements for image acquisition as revealed by our phantom experiments, apply fully to the clinical settings. Therefore, care must be taken to have ideal imaging conditions, in particular, good spatial resolution and frame rates as high as possible. Since such conditions can not always be found in clinical patients, a limited feasibility of the approach in a routine setting must be expected.

In this study we used phantoms for the validation of PIV echocardiography which provided a defined two-dimensional pattern of speckle motion. In clinical practice, out-of plane motion of contrast speckles may lead to inaccuracies in the assessment of complex vortex structures in human heart chambers [19, 20]. Interpretation of 2D tracking results must always consider, that at best the in-plane component of a 3D flow structure can be assessed. Three-dimensional echocardiography may help to overcome this limitation, but volume rates and spatial resolution of current machines are not sufficient for flow tracking in humans.

Our phantoms provided close-to ideal image quality without artefacts and homogeneous distribution of speckles. Less favorable scanning conditions in cardiac patients and inhomogeneities in contrast distribution may lead to tracking problems and subsequent misinterpretations of the flow field.

In our study, speckle patterns were generated by solid bodies, while in the clinical application they are generated by a non-Newtonian fluid. Together with the spatial character of fluid vortices, this may limit applicability of the model to the in vivo situation.

Given the underlying methodology, it must be assumed that tracking results do also depend on other imaging parameters, such as speckle distribution and density [20]. Therefore the sensitivity of the algorithm to the number of speckles per unit area was not evaluated. The current setup was not suited to investigate this relation. Furthermore, it is unclear how the software determines the periphery of vortex structures, since velocities are gradually declining when increasing the distance from the center. Further studies are needed to address those questions.

Particularly in diastole, kinetic energy of the blood entering the ventricle should be stored and the blood flow should be re-directed for ejection with a minimum of energy loss. A vortex structure appears ideally suited for this and may help to maximize ventricular efficiency. Therefore, echocardiographic PIV can provide new insights into diastolic function and dysfunction of the heart chambers. Further, the method might help to better understand the effect of regional myocardial dysfunction, e.g. after myocardial infarction, or help to optimize surgical interventions, such as valve replacements.