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Experimental Studies |
1 From the Department of Radiology, University of Michigan Hospitals, University Hospital B1Dd 502/0030, 1500 E Medical Center Dr, Ann Arbor, MI 48109-0553. Received October 1, 1998; revision requested December 10; revision received January 20, 1999; accepted February 8. Supported in part by a research gift from General Electric, U.S. Army Medical Research and Materiel Command, DAMD 17-94-J-4144. Address reprint requests to J.M.R. (e-mail: jrubin@umich.edu).
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Abstract |
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 TOP Abstract IntroductionMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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MATERIALS AND METHODS: In vivo and in vitro studies were performed. A tube with flowing saline solution containing contrast agent was positioned horizontally across a US image. The amount of decorrelation between a series of images was recorded. The flow profile across the tube was generated by averaging the decorrelation values and was compared with a Doppler frequency shift image. In addition, B-mode images of six rabbit kidneys were obtained during and after intravenous injection of contrast agent. Images were analyzed to compute the correlation between successive points in time.
RESULTS: The velocity profiles across the tube were parabolic, with the fastest flow rates measured in the center of the tube. In the rabbit kidneys, measurements indicated the largest decorrelation rates occurred in the larger vessels. The cortical decorrelation rates were significantly slower than those for the hilar vessels (P < .05) and were relatively angle independent.
CONCLUSION: Decorrelation flow measurements can be used to estimate flow in vitro and in vivo similar to measurements obtained with Doppler US but with less angle dependence. These measurements could lead to a US perfusion technique.
Index terms: Blood, flow dynamics, 9*.12983, 9*.129883 • Blood vessels, US, 9*.12983, 9*.12988 • Ultrasound (US), contrast media, 9*.12988 • Ultrasound (US), Doppler studies, 9*.12983 • Ultrasound (US), experimental studies, 9*.12983, 9*.12988 • Ultrasound (US), physics, 9*.12983, 9*.12988 • Ultrasound (US), technology, 9*.12983, 9*.12988
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Introduction |
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Decorrelation is caused by a change in the speckle pattern in a given sample volume determined by the dimensions of the ultrasound beam and the pulse length or the three-dimensional point spread function. Ideally, this speckle pattern change would be caused completely by fluid movement through the sample volume. If the point spread function is made spherically symmetric, the mean transit time should be nearly independent of flow direction; therefore, the decorrelation might be made angle independent. In any case, it is highly possible that this angle dependence is not as big an effect as the cosine dependence of Doppler.
Gray-scale speckle decorrelation also has been proposed and used to detect motion in B-mode imaging (2,3). In addition, speckle decorrelation has been used to monitor the motion of scan heads to produce three-dimensional US images without additional hardware requirements (4–7). In these techniques, the rate of speckle decorrelation is related to the velocity of the scan head in the elevational direction. For the detection of blood flow, the process is essentially inverted. The transducer is fixed in position, and the motion of blood at any given position in the scan plane will result in a fluctuation in the signal amplitude, which can be related to the velocity.
The complication is that the relative low backscatter coefficient for blood produces very little signal compared with that for soft tissue, with the subsequent low signal-to-noise ratio confounding earlier preliminary attempts to use this method (3). Yet even with these problems, the decorrelation of blood signal in normal B mode has been demonstrated by Bamber et al (3) by examining flow in the inferior vena cava. However, this may have been an especially good target because the backscatter of slowly moving (in the presence of low shear) venous blood is higher owing to rouleaux formation, which produces a relatively strong signal (8–12).
One possible solution that would make the B-mode techniques more universal is to use US bubble contrast agents to overcome some of these difficulties. The signal amplitude of blood should be sufficiently high in the presence of contrast agent, and the agent is not expected to experience rouleaux that might complicate the amplitude dependence of the backscatter. Decorrelation imaging with contrast agents could then combine the high spatial resolution and frame rate of B-mode imaging to provide the flow detection and velocity information of Doppler imaging.
The hypothesis behind the experiments described herein is that the speckle produced by the bubbles in the contrast agent will decorrelate as a function of velocity. We investigated this hypothesis in vitro by using flow tubes and in vivo in a rabbit kidney model with the hope that this measure could lead directly to a US perfusion estimate.
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MATERIALS AND METHODS |
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The time intervals we use are called "lags"; a lag is a frame-to-frame increment for which we assumed a stationary process. For example, the correlation between frames 1 and 2, 2 and 3, 3 and 4, and so on are referred to as one lag. Correlations based on frames 1 and 3, 2 and 4, 3 and 5, and so on are called two lags, and so forth.
In Vitro Experiments
To examine the relationship between decorrelation with contrast agents and flow velocity, measurements were performed on a flow system containing a 7.8-mm-diameter dialysis tube (Spectra/Por Type 2; Spectrum, Houston, Tex) at mean flow velocities of 0, 0.48, and 1.39 cm/sec (Fig 1). Mean flow velocities were measured on the basis of volume flow estimates by using a graduated cylinder. The zero flow data set was also obtained to determine how much decorrelation occurs merely in the presence of bubbles. A tube was chosen to produce laminar flow with a well-known parabolic flow profile, which provided a variety of known velocities on one image. A bubble trap was used to collect any large bubbles that appeared during filling, and it served as a "capacitor" to eliminate the pulsatility of the peristaltic pump that was used. The contrast agent, lipid-stabilized perfluorocarbon-filled microbubbles (MRX-115; ImaRx Pharmaceutical, Tucson, Ariz), was diluted one part to 105 with saline solution for circulation. A 10-MHz linear array on a US scanner (VST; Diasonics, Milipitas, Calif) was used to image perpendicular to the flow direction of the contrast agent, with the output power of the scanner turned down 10 dB to reduce bubble attrition and acoustic radiation force due to the ultrasound beam.
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is the mean intensity over the window, lag is the number of frames between images being compared, max_lag is the largest lag computed, and N is the total number of frames in the data set. The autocovariance values for each pixel were computed over a user-defined spatial window (the first summation) centered on the current pixel, and each lag was normalized by the zeroth lag or variance that generated a correlation coefficient, CN. The spatial window used was 21 x 5 pixels, with the longer dimension oriented along the flow direction. The correlation coefficient is a number between -1 and 1, which is then sign inverted and scaled from 0 to 255 for purposes of display. Thus, a high correlation coefficient, CN = 1, corresponds to 0, and a negative correlation coefficient, CN = -1, corresponds to 255. In this way, a decorrelation image is produced for each time lag, and the higher the decorrelation is, the whiter the gray value is. As mentioned earlier, this inverted gray-scale display provides a means to image a relative, qualitative decorrelation map. We used it because it could easily be assigned to the 0 to 255 gray-scale distribution.
The flow profile across the tube was generated by averaging the decorrelation values along the length of the tube, which reduced the two-dimensional image to a one-dimensional profile with the percentage of decorrelation calculated as 1 - CN. Similarly, averaging of the frequency shift values along the length of the tube was performed for comparison. Doppler images from the horizontal tube were obtained by using the beam steering of the US unit.
In Vivo Experiments
Initial animal trials were designed to demonstrate the variation of decorrelation rates in the kidney. We performed experiments in six adult female New Zealand albino rabbits (Kuiper Rabbit Ranch, Gary, Ind) that weighed 2.0–3.7 kg and that were anesthetized with either xylazine hydrochloride (Rompun [10 mg per kilogram of body weight injected subcutaneously]; Mobay, Shawnee, Kan) and ketamine hydrochloride (Ketaset [50 mg/kg injected intramuscularly]; Fort Dodge Animal Health, Fort Dodge, Iowa) or isoflurane (Isosol [1.5%–2.0% inhalation with O2]; Medeva Pharmaceuticals, Rochester, NY). MRX-115 was administered through the ear vein catheter, either as a 50 µL/kg bolus or diluted in 10 mL of saline solution and infused at 1 mL/min. Images were then obtained and processed with either one of two methods outlined later to detect motion associated with the bubbles. At the conclusion of the experiment, the rabbits were killed, according to approved protocols, with an overdose of pentobarbital sodium (Beuthanasia-D; Schering-Plough Animal Health, Kenilworth, NJ) injected intravenously while they were still anesthetized. The experiments were conducted in an ethical and humane fashion, and experimental design was approved by the University of Michigan's committee on use and care of animals in accordance with U.S. government guidelines.
The set of in vivo images for the first rabbit was processed in 5 x 5-pixel regions of interest, as opposed to the 21 x 5-pixel region of interest for ex vivo experiments. This was done to maintain reasonable spatial resolution for this initial trial. Also, by using a standard algorithm in the AVS software package, an in-plane two-dimensional cross-correlation was performed between adjacent frames to correct for respiratory motion prior to the decorrelation calculation. A region of the image that enclosed the kidney was used to determine the relative axial and lateral shift necessary to maximally align the individual images in these two directions. The residual decorrelation was assumed to be due to flow, although soft-tissue motion in the elevational direction could contribute. The volume data were adjusted for the axial and lateral motion, and then a decorrelation rate was measured over the time series.
The group of image regions of interest were analyzed to compute the correlation between successive regions of interest in time: region of interest 1 correlation to region of interest 2, region of interest 2 correlation to region of interest 3, and so on for a one-step correlation value at each image location. As mentioned earlier, this is referred to as the first time lag correlation. The process is repeated for two lag correlations, three lag correlations, and so on.
The remaining in vivo studies, in five rabbits, were performed with a US scanner (Logiq 700; GE Medical Systems, Milwaukee, Wis), and images were processed for decorrelation in a slightly different manner. We used a 739 (GE Medical Systems) linear array probe that scanned at 9 MHz. The probe was attached to an external frame that held the probe in a fixed position on the rabbit's body during the experiments. Either the right or left kidney was imaged, depending on access. We scanned with no frame averaging and the lowest power output possible. Gray-scale images were stored on cine loop at 30 frames per second during the time in which the level of contrast agent had reached a steady state. Then a 4-second segment was copied to the machine's hard disk for storage and later processing.
Portions of the time series during which the rabbit was stationary without respiratory motion (nominally half-second intervals) were segmented out for analysis. For each pixel in the first frame, the temporal autocovariance was computed and normalized by means of the variance to produce a correlation coefficient as noted earlier. A mean correlation function was computed for all the stationary time segments, which formed a lag array with values ranging from 1 to -1 for each pixel. For each lag, a corresponding image can be formed and displayed by scaling the correlation value from 0 to 255 as described earlier. Again, rapidly decorrelating pixels will appear bright, whereas slowly decorrelating pixels are dark.
In the cortex, blood flows largely radially, and consequently a full range of angles between flow direction and the ultrasound beam is present in a single scan (14, 15). Hence, the normal kidney anatomy presents an opportunity to evaluate in vivo the angle dependence of the decorrelation technique. This can be done by examining the decorrelation rates in the cortex region of the lag 1 images. A semiautomatic segmentation algorithm was used to select the kidney cortex. The lag image was first smoothed with a 15 x 15-pixel Hamming window. A binary mask was then formed to eliminate quickly decorrelating pixels associated with major blood vessels. On the basis of the histogram of the smoothed lag image, the 5% lowest decorrelation values were masked out. A second mask was then applied to isolate the cortex. The outline of the kidney was hand selected on the basis of the original B scan, and a morphologic operator, "shrink," was applied to form a strip approximately 25 pixels wide, which corresponded to the cortex. The intersection of the two masks formed the final binary cortex mask.
To examine the decorrelation angle dependence without computing vectors normal to the kidney border, we devised a simpler projection technique. The cortex mask was overlayed on the lag image, and the mean correlation value was computed along columns one pixel wide (pixel width = 105 µm). If the velocity estimate based on decorrelation is angle dependent, the resultant plot should show progressively higher correlation averages as one approaches the upper and lower poles where the blood flow is perpendicular to the beam. This is because the speckle will remain correlated longer if the decorrelation is slower (ie, similar to Doppler angle dependence). If there were no angle dependence, the average correlation values for these columns across the kidney would be perfectly flat.
Statistical comparisons between cortical and hilar vascular decorrelation rates were performed by using a two-tailed Student t test. A P value less than .05 was considered to indicate a statistically significant difference.
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RESULTS |
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DISCUSSION |
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The results presented indicate that the use of US gray-scale speckle decorrelation with bubble contrast agents may be useful for measuring blood flow in vivo. The results for the tube experiment show that the anticipated parabolic flow profile is realized and corresponds to the Doppler flow measurement. In the case of the decorrelation technique, measurements were made with the flow perpendicular to the ultrasound propagation direction, which is a limitation in Doppler flow imaging. In addition, decorrelation with contrast agents can be used to detect very low flows. In our study, the flow tube measurements were performed at a pulse repetition frequency of 100, which would generally be much too slow for in vivo detection owing to the associated slow frame rates and problems with soft-tissue motion.
Although not investigated in these experiments, the potential exists for decorrelation measures to be made angle independent by adapting the point spread function of the imaging beam to create uniform decorrelation rates in all three dimensions. If so, the angle dependence of the measure should be minimal. There is, however, recent evidence that decorrelation is angle dependent to some degree (18), and this angle dependence will have to be compensated for if this is to be an advantage over Doppler sampling. As noted earlier, at least in this study, the angle dependence appears to be relatively small compared with standard Doppler angle dependence; and there is clearly detectable flow at all angles, whereas Doppler is well known to lose signal at 90°, with an expected decrease in frequency shift of 50% at 60°. Measurements of the beam profile for our GE 739 linear array scanner head for the ratio of axial to lateral beam widths in the focal zone is about 50% (T.A.T., personal observations). This is very similar to our maximum deviation measurement.
The method used to generate a symmetric sample volume would be straightforward. By increasing the pulse length (ie, narrowing the bandwidth of the transmission), it would be possible to degrade the axial resolution and thus approach the lateral and elevational resolutions. If the lateral resolution needed to be compromised to approximate the elevational focusing, this could be accomplished by decreasing the aperture. Thus, it would be possible to approach an isotropic sample volume. As lateral and especially elevational focusing improves with one-and-a-half- and two-dimensional arrays, the amount of bandwidth narrowing and aperture reduction would become less and less with time. Further, it should be noted that the amount of bandwidth narrowing, especially in the region of best elevational focus, required here might still be less than that used in standard color Doppler flow in which the bandwidth is narrowed enough to clearly degrade the spatial resolution of color pixels. This is why the color pixels are much larger than gray-scale pixels in standard color Doppler flow images.
It is worth noting that decorrelation provides no directional information in general. As noted in flow phantom experiments, velocity information can be obtained with a priori knowledge of the flow direction (1). However, speckle decorrelation can be used only to estimate the rate at which material moves through a sampling site, an advantage of which is the ability to measure the flow through the ultrasound beam in any direction. Thus, the measure is in some sense three-dimensional, since it is influenced by and measures flow in all directions. In addition, in many cases directional information is not the important quantity, such as in perfusion, in which the inverse of the decorrelation rate would correspond to the mean transit time through the tissue (1).
Mean transit time is a highly sought-after quantity of flow, and estimating it usually requires a technique involving the administration of a bolus of contrast agent (19,20). Boluses have the well-known problems of spreading and distortion, which can severely complicate estimates of mean transit time. A method, such as speckle decorrelation, for easily estimating mean transit time without requiring a bolus of contrast agent is hence attractive. Further, once an estimate of mean transit time has been obtained, one needs only an estimate of the amount of blood in tissue to have a perfusion measure. Techniques for making such estimates of fractional moving blood volume have already been proposed (21,22). These measurements have been limited by rouleaux formation by red blood cells, which is a problem that does not arise with contrast agents.
The initial animal experiments presented indicate that the decorrelation rate of contrast agents scales with speed: larger hilar vessels decorrelate faster than the renal cortex (Table 1) (P < .05). We use speed here, since no directional information is obtained. This would imply that a measurement potential exists, but it remains to be determined if the actual speed can be extracted. As noted, decorrelation did not scale perfectly with velocity in the flow tube. This was almost certainly owing to the changing shape of the velocity profile with increasing flow. As the flow increases, the profile becomes steeper across the tube—the velocity gradient across the flow increases. This increased gradient means that each voxel contains more than one velocity component. These components will dephase within each voxel over time and cause the speckle to decorrelate before it actually leaves the voxel being imaged. Thus, the detected decorrelation rate will cause overestimation of the speed. This effect will be less pronounced in small vessels in which perfusion measurements are of greatest interest.
Other causes of signal dephasing such as bubble destruction could also confound any use of decorrelation times as a perfusion measure. Contrast agents can be destroyed by ultrasound fields of the types used in medical imaging (23). Decorrelation may also be influenced by such effects as bubble oscillations, translation due to acoustic radiation force, and brownian motion within the sample volume. Decorrelation would cause misinterpretation of these as bulk flow. If this method becomes clinically useful, bubbles with very stable shells will be useful.
Our preliminary results here suggest that, at least in flow tube experiments, bubble destruction and translation due to radiation forces are small contributors to decorrelation compared with true flow, at least at the pressure amplitudes used here (Fig 4). Further, it is worth noting that when the speckle in a pixel becomes nearly fully decorrelated, the calculated decorrelation begins to show a statistical fluctuation around total decorrelation or, equivalently, fluctuations around a correlation coefficient of zero. Hence, it is possible to obtain small negative correlations (ie, decorrelation values of more than 100%, as shown in Figure 4). Such problems would be easy to avoid in practice by either measuring a decorrelation rate to some nonzero value, such CN of 50%, as we did in Table 1, or with faster gray-scale sampling, by fitting the decorrelation curve with an exponential or Gaussian curve and using the calculated time constant as the decorrelation rate (1,5).
One curious effect was the axisymmetric decorrelation noted in the tube when there was no flow (Fig 4). At first glance, one would expect a more uniform distribution, although there is never any flow at the walls. We are not certain of the cause of this phenomenon. Although the pump was turned off at the time of this measurement, we cannot guarantee that there was absolutely no flow, particularly at this very low level. Further, there may be very small oscillations in the system that would manifest in this way. Although this plot looks like it shows laminar flow, there is really no directional information displayed here, so periodic oscillations would look just like this. Structured decorrelation in a flow tube such as this is an important issue to resolve. The decorrelation rates in Figure 4 are much lower than those caused by even the very slow flow rates we studied, however, and these results suggest that random bubble motions and destruction need not seriously degrade decorrelation measurements made in flow liquids.
It should be mentioned that this method is fundamentally different than the well-known speckle tracking and two-time correlation techniques used for blood velocity measurements (24–26). In those methods, spatial or temporal correlations on reflected signals are performed to try to map the displacement of moving targets such as red blood cells to estimate their velocities. A reference is moved in typically either one or two dimensions to try to track the new location of the scatterers that produced the reference. In the decorrelation method, there is no tracking involved. All one does is estimate the rate of change of the scattering intensity at given positions during the sampling period. It is, in some sense, a much simpler process.
Practical application: Although still in the experimental stage, speckle decorrelation flow measurements could lead to a perfusion measurement in tissue, a highly sought-after parameter. The speckle decorrelation rate is directly related to the mean transit time in tissue, which is one-half of the perfusion measure, and by using US contrast agents, this measure now appears to be obtainable. The advantages of speckle decorrelation over standard administration of a bolus of contrast agent and the Doppler method for estimating mean transit time include that it is relatively angle independent compared with Doppler, it is inherently a three-dimensional measurement, and it can be performed by using continuous infusions of contrast agent. In addition, the use of contrast agents has the benefit of improving the fractional blood volume measurement, the other half of a perfusion estimate, by removing the effects of rouleaux.
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Footnotes |
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2 Current address: Hospital of Special Surgery, New York, NY. 
9*. Vascular system, location unspecified.
Author contributions: Guarantors of integrity of entire study, J.M.R., J.B.F.; study concepts, J.M.R., J.B.F., R.S.A., P.L.C.; study design, J.M.R., J.B.F., A.P.M.; definition of intellectual content, J.M.R., J.B.F.; literature research, J.M.R., J.B.F.; experimental studies, J.M.R., J.B.F., R.T.R., S.N.K.; data acquisition, J.M.R., J.B.F., R.T.R., S.N.K.; data analysis, J.M.R., J.B.F., T.A.T., A.P.M.; statistical analysis, J.M.R., J.B.F., T.A.T., A.P.M.; manuscript preparation, J.M.R., J.B.F.; manuscript editing, J.M.R., J.B.F., T.A.T., R.S.A.; manuscript review, J.M.R., J.B.F., T.A.T., R.S.A., P.L.C.
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References |
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