Background
In this study, the functionality of echocardiographic particle imaging velocimetry (E-PIV) was compared with that of digital particle imaging velocimetry (D-PIV) in an in vitro model. In addition, its capability was assessed in the clinical in vivo setting to obtain the ventricular flow pattern in normal subjects, in patients with dilated cardiomyopathy, and in patients with mechanical and bioprosthetic mitral valves.
Methods
A silicon sac simulating the human left ventricle in combination with prosthetic heart valves, controlled by a pulsed-flow duplicator, was used as the in vitro model. Particle-seeded flow images were acquired (1) using a high-speed camera from the mid plane of the sac, illuminated by a laser sheet for D-PIV, and (2) using a Siemens Sequoia system at a frame rate of 60 Hz for E-PIV. Data analysis was performed with PIVview software for D-PIV and Omega Flow software for E-PIV. E-PIV processing was then applied to contrast echocardiographic image sets obtained during left ventricular cavity opacification with a lipid-shelled microbubble agent to assess spatial patterns of intracavitary flow in the clinical setting.
Results
The velocity vectors obtained using both the E-PIV and the D-PIV methods compared well for the direction of flow. The streamlines were also found to be similar in the data obtained using both methods. However, because of the superior spatial resolution of D-PIV, some smaller scale details were not revealed by E-PIV. The application of E-PIV to the human heart resulted in reproducible flow patterns in echocardiographic images taken within different time frames or by independent examiners.
Conclusions
The E-PIV technique appears to be capable of evaluating the major flow features in the ventricles. However, the bounded spatial resolution of ultrasound imaging limits the small-scale features of ventricular flow to be revealed.
Left ventricular (LV) fluid dynamics represent an elegant flow phenomenon, starting with the transmitral jet reaching a maximal velocity of about 100 cm/s in traveling a distance as short as only a few centimeters. This volume of blood must then turn around to exit the left ventricle via the aortic valve within a fraction of a second while maintaining its initial high velocity. For this to happen properly, nature has chosen a vortex flow (a swirling motion of fluid), which is developed during diastole, to redirect the transmitral flow toward the LV outflow tract. This track of motion guarantees efficient transfer of the fluid momentum and minimizes the ventricular energy dissipation.
Despite improvements in intraventricular flow visualization by means of advanced noninvasive imaging modalities , experimental and numerical models, several aspects of the corresponding fluid dynamics phenomena are still unclear. The key reason for the lack of quantitative information concerning cardiac flow is the lack of technology that can reliably map the spatial and temporal details of the flow while being feasible in routine clinical use.
Color Doppler imaging, as a tool to obtain intracardiac flow information, considers only a single component of blood velocity along the transducer scan line and does not provide quantitative information with respect to vortex formation, recirculation areas, and flow stagnation zones. Because of these limitations, color Doppler imaging may not provide adequate information for either the reconstruction of velocity vector fields or the actual direction of streamlines. Several attempts have been made to incorporate quantitative fluid dynamics into echocardiography using particle-tracking algorithms. This echocardiographic approach has received further attention in the clinical setting, mainly due to its higher image quality and potential for the assessment of intraventricular blood flow. The particle-tracking methods are mostly based on well-known optical imaging techniques of particle image velocimetry (PIV) previously described by Adrian and further developed by Willert and Gharib to measure two-dimensional and three-dimensional flow velocity fields.
Although the application of PIV to echocardiography seems promising, and results appear to be qualitatively meaningful, the acquired data in clinical settings has yet to satisfy the minimal theoretical requirements. Careful attention is needed to systematically evaluate the accuracy of echocardiographic PIV (E-PIV) for diagnostic purposes. In this study, we compared the results obtained using E-PIV with those simultaneously acquired by digital PIV (D-PIV) from an in vitro model of the left ventricle that reproduced flow conditions similar to the normal human heart. In addition, we used E-PIV to evaluate a number of different clinical subjects to test the reproducibility and the operator interdependency of the technique. The aim of the present study was to assess the reliability, accuracy, and limitations of E-PIV for the quantification of ventricular flow from the postprocessing of ultrasound data. Examples of potential clinical applicability are also presented.
Methods
Techniques that are based on PIV or, more generally, on optical flow measurements have been proven successful in several applied fields of science, ranging from turbulent fluid dynamics to optical motion recognition. The main challenge in the application of PIV to echocardiography, besides image quality (low signal-to-noise ratio), is the low ratio of spatial resolution to temporal resolution, which prevents the interpretation of the entire range of velocities in the human heart. Good results can principally be obtained using direct PIV when the frame rate is high enough to reduce this limitation. The approach described here introduces a carefully developed hierarchical algorithm that allows for the identification of velocity vector direction despite the deficiency of accurate velocity magnitude. The computed results were then rearranged in terms of fluid dynamics parameters such as vorticity, which is a physical term to properly describe intraventricular flow patterns.
In Vitro Experimental Model
For the purpose of this study, we used a left-heart pulsed-flow simulator system. The system comprised a silicon heart with adult human dimensions suspended in a pressurized Plexiglas (Altuglas International, Philadelphia, PA) container. A 23-mm Carpentier-Edwards PERIMOUNT bioprosthetic heart valve (Edwards Lifesciences, Irvine, CA) and a 21-mm Sorin Biomedica Carbocast mechanical heart valve (Carbomedics, Austin, TX) were placed in the mitral and aortic positions, respectively. The periodic, pulsatile flow in the circulatory system was generated as the response of the ventricular sac to the input waveform provided by the pump. The waveform reproduced a systolic ratio (the fraction of time in a cardiac cycle during which the left ventricle is in systolic phase) of 40%.
Distilled water was used as the circulating fluid, and the system time scale was increased (about 2.5 times) with a heart rate of 30 beats/min to compensate for the viscosity differences between blood and water. This ensured similarity between the model and the human heart at 75 beats/min, with the same Reynolds number and Strouhal number. For optical and ultrasound acquisitions, flow was seeded with neutrally buoyant particles (diameter, 100-120 μm) illuminated with a laser light sheet on a plane containing both mitral and aortic valves. Pairs of optical images, separated by a short time interval, were acquired with a high-resolution monochrome digital camera with a charge-coupled device (30 frames/s; resolution, 768 × 480; TM-9701, PULNiX America, Inc, Sunnyvale, CA) with a rate of 15 pairs/s.
D-PIV
D-PIV is an optical method used to obtain flow characteristic information (eg, velocity and vorticity fields) from the analysis of a pair of images to determine the displacement field of the particles in the field of view (sampling window) by cross-correlating pixels in a subsection of two images.
D-PIV acquisitions and processing were performed with intervals of 1, 3, and 5 ms to verify the convergence of results. The time interval between the image pairs is crucial for the accuracy of D-PIV results, because it corresponds to the expected particle displacements. Limitations include too large or too small displacements, which are difficult to detect. Data analysis was performed with PIVview software (PIVTEC GmbH, Goettingen, Germany). Eventually, 3 ms interval was determined as the optimal value for this experiment and was used for further processing. The velocity vector components were obtained on a regular grid of 74 × 61 points, separated by 1.778 mm, covering most of the LV space. Four consecutive beats were processed, and the results for the average heartbeat were used in the analysis. An example of the computed velocity field superimposed on the image is shown in Figure 1 (left).
In Vitro Ultrasound Image Acquisition
An Acuson Sequoia c512 and the 4V1c transducer (Siemens Medical Solutions, Mountain View, CA) were used for the experiment. Ultrasound imaging was performed at a harmonic frequency of H4.25 MHz and a frame rate of 35 Hz. Digital loops of 3 cycles were acquired from the LV system described earlier simultaneously with D-PIV using the same nanoparticles.
The ultrasound transducer was secured externally to the Plexiglas chamber in an apical LV view. Care was taken to have the scan plane coincide with the optically acquired laser sheet; however, this was done visually since no automatic control was in place. Image optimization controlled the artifacts hard interfaces (Plexiglas, valves) and water-silicon-water interfaces (LV chamber). An example of the acquired image is shown in Figure 1 (right).
In Vivo Ultrasound Image Acquisition
Echocardiography with contrast agent imaging was performed on five healthy volunteers by two independent examiners within two consecutive days and repeated for one volunteer at a 3-month interval. The Acuson Sequoia c512 and the 4V1c transducer were used to image all volunteers and patients. Imaging was performed at harmonic frequencies of H3.25, H3.75, and H4.25 MHz; frame rates of 60 to 80 Hz; a mechanical index of 0.6 to 0.7; and dynamic ranges of 45 to 55 dB. The acoustic focus was placed at the mitral annular level. Contrast enhancement was produced by intravenous bolus administration of 0.1 to 0.2 mL lipid-shelled octafluoropropane microbubble contrast agent (Definity; Lantheus Medical Imaging, North Billerica, MA), diluted in 10 mL of saline solution. Acoustic captures of three consecutive heart cycles for the apical 3-chamber (A3C), apical 2-chamber (A2C), and apical 4-chamber (A4C) projections were acquired ( Video 1 ; 
view video clip online). During image acquisition, care was taken to maintain a constant homogenous contrast agent concentration in the left ventricle for visualization of swirling flow. In addition, five patients with dilated cardiomyopathy (DCM) and eight patients with prosthetic heart valves (four bileaflet Carbomedics, four biologic Medtronic Hancock; Medtronic, Inc, Minneapolis, MN) were imaged. Data were acquired using the same ultrasound system and imaging acquisition protocol. The patient study was performed with institutional review board approval, and all patients provided written consent.
E-PIV
E-PIV data analysis was performed using Omega Flow software prototype version 4.0 (Siemens Medical Solutions). To initialize the procedure, the examiner was required to trace the contour of the LV cavity by the interface; this contour was then tracked in other frames to create a boundary for the region of analysis. The processing results were initially displayed as velocity vectors overlaid on the contrast-enhanced B-mode images. The instantaneous vorticity analysis was reviewed frame by frame. Finally, the steady streaming vorticity field was evaluated by taking the time-average of the velocity field during one heartbeat. The steady streaming flow pattern represents the net dominant flow motion and allowed visualization of the location and shape of intraventricular vortices and circulatory pattern. The software performed dedicated PIV processing optimized for echocardiography. The technical details of this PIV method and the justifications are provided in Appendix A .
Fluid Dynamics Analysis
The resulting velocity sequences were analyzed to derive further spatial flow characteristics for better characterization of the flow patterns. The fundamental quantity that describes the motion of the fluid is represented by the vorticity defined as the tendency of fluid elements to spin; more precisely, vorticity can be related to rotation of fluid elements and the formation of circulatory areas. Quantitative parameters of the intraventricular vortex were also extracted on the basis of the vorticity. The details of the mathematical analyses are provided in Appendix B .
Results
In Vitro Results
The velocity fields computed by D-PIV are shown in Figure 2 (top row) at the peak of the filling wave, during inflow deceleration, at late diastole, and at the beginning of systole, respectively. The corresponding velocity fields obtained by E-PIV are also shown in Figure 2 (bottom row). Despite the differences in spatial resolution, dynamic range, and velocity accuracy between the two methods, the main physical features of intraventricular flow could be outlined. The flow presented an intense transmitral jet that reached the septum, with two circulatory components on both sides ( Figure 2 , early diastole); the flow then moved along the septum toward the apex (mid-diastole), where the apical vortex persisted within the rest of diastole (late diastole), and finally weakened and moved toward the base at the beginning of contraction (early systole). The image quality of D-PIV allowed the evaluation of sharp spatial gradients, whereby substantial flow changes could be observed within the window of one or two grid points.
To quantitatively compare D-PIV and E-PIV for local, instantaneous velocity magnitudes, it was necessary to convert the results of both methods on the same space-time computational grid. To do this, at every instant, the D-PIV velocity fields were sampled on the E-PIV (37 × 29) spatial grid using bilinear interpolation. Prior to this, the D-PIV velocity fields were preliminarily filtered with a 2-dimensional Gaussian isotropic filter of 10 mm in width to eliminate the small-scale fluctuations that were not present in the ultrasound results and to allow a punctual comparison. The results presented below were not considerably affected by changing the filter width from 7 to 10 mm and to 15 mm, respectively. Sampling time was also different for both methods (15 and 68 frames/beat for D-PIV and E-PIV, respectively). To accurately compare the two methods, Fourier time decomposition was performed on both fields, followed by reconstruction at 16 time-instants by 8 Fourier harmonics.
A total of 7331 velocity vector magnitudes (on about 460 spatial locations at 16 time instants) were compared. The statistical distribution of the difference between the velocity magnitudes computed by E-PIV and D-PIV (ie, the error in the absolute velocity) is shown in the histogram of Figure 3 A . The error is reported as a percentage of the average velocity. The distribution was peaked at zero (mean value, −2.45%) with a moderate dispersion about the mean value (standard deviation, 80%). The inset in the same panel shows a polar histogram of the error in the direction of the computed velocity vectors. The error of flow direction was centered at zero, with a moderate dispersion in the range of ±30°, indicating an overall accuracy of estimated velocity direction and the streamlines. The histograms in Figure 3 B show the discrepancy in the magnitude of velocities evaluated only in those points for which the D-PIV velocity was higher than the median value (3665 samples). The histogram is peaked toward the negative (mean value, −28%) and negatively skewed. The inset shows that the error in direction was reduced.
Further analysis was performed to verify the reproducibility of E-PIV in the controlled laboratory setting. With the apparatus running under the same imaging conditions, four additional sequences (two 3-beats and two 2-beats) were acquired and processed. The flow in all the sequences was found to be equivalent as all four steady streaming fields were about equal. The vortex parameters, such as the sphericity index (SI) and vortex pulsatility coefficient (VPC), differed by <1% (see Appendix B ).
In Vivo Results
The prototype Omega Flow software was used to process all ultrasound image sequences. The normal volunteer data were processed by two examiners blinded to each other’s results. The data were also analyzed by the same examiner after a 6-month interval. The results for normal volunteers indicated comparable flow patterns for the same volunteer in the same views on the same day, the subsequent day, and within a 3-month interval. Comparable flow patterns were also similar for the same projections between volunteers. Vortex flow direction for the A4C view showed counterclockwise rotation, while the A3C view showed clockwise rotation for all normal volunteers ( Video 2 ; view video clip online.). Flow patterns were also similar for the same volunteers when analyzed by two different examiners. Examples of comparisons are shown in Figures 4 and 5 . The quantitative comparisons for the vortex structure were performed on the basis of (1) the geometric index of Sphericity (SI), which is a dimensionless measure of the mean vortex shape, and describes the ratio of the vortex’s long axis to its short axis, and (2) the dynamic parameter of vortex pulsatility coefficient (VPC), which is a dimensionless measure of vortex unsteadiness as defined further in Appendix B . The average values and the standard deviations of the SI and the VPC for the five normal volunteers in the A3C views were 2.38 ± 0.35 and 0.63 ± 0.21, respectively. The interoperator variability revealed small discrepancies as low as 0.44 ± 0.48 for the SI and 0.04 ± 0.06 for the VPC, respectively. Additionally, the intraoperator variability was 0.04 ± 0.05 for the SI and 0.06 ± 0.15 for the VPC.
