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The Clinical Center and the National Cancer Institute, National Institutes of Health, Bethesda, Maryland
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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Key Words: PET • [15O]water • parametric image • tumor blood flow
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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In this study we used a dynamic acquisition protocol that, in conjunction with appropriate kinetic models, enabled the quantitative measurement of tumor blood flow. The standard method for analyzing such data (which we refer to as the region-of-interest [ROI] method) is to draw an ROI around the tumor, generate a time–activity curve from this region, and then apply a kinetic model to the time–activity curve to measure flow and other parameters described by the model. One of the problems with the ROI method is that each time a new region is to be analyzed, the entire set of dynamic data must be used to produce the time–activity curve. If large numbers of regions are to be analyzed, this produces equally large numbers of time–activity curves, and the resulting data are often difficult to present in a meaningful manner. In addition, identification of the tumor ROI is not trivial and, even if additional information is available from other modalities, the definition of ROIs may be prone to errors. Finally, most blood flow models assume that blood flow is uniform throughout the tumor ROI, which may not be true. To help overcome these problems we have developed a parametric imaging approach in which the model fitting is performed on a pixel-by-pixel basis, resulting in images that directly reflect regional blood flow. Parametric images have been used widely in studies of cerebral blood flow with [15O]water (12–15) and also in other studies of the brain—for example, with [11C]flumazenil (16) and [18F]fluoro-L-dopa (17). The technique has also been used in cardiac studies with FDG (18), renal studies with [13N]ammonia (19), and tumor studies in the liver with FDG (20).
The application of the parametric imaging technique to tumor blood flow studies using [15O]water raises several interesting issues. Although the kinetic model used in most water studies is a standard single-compartment model, several different variations to this model have been developed, each of which has its own advantages in different situations. In studies of the brain, a formulation of the model that is frequently used allows measurement of both flow and volume of distribution. This formulation derives flow information primarily from the influx phase of the dynamic data and is well suited to brain studies in which organ motion can be minimized. In studies of the heart, however, there can be significant partial-volume effects caused by motion of the myocardium and by the fact that the myocardial thickness (typically 
10 mm) is comparable with the resolution of most PET scanners. An alternative formulation of the model used for cardiac studies (21) assumes that the volume of distribution in the myocardium is known and permits flow to be computed in such a way that it is, in principle, independent of partial-volume effects. This formulation derives flow from the efflux phase of the dynamic data. In addition, so-called spillover terms are often introduced into the model to account for contamination of the tissue time–activity curves by activity in nearby blood vessels.
The optimum formulation of the blood flow model for the measurement of tumor perfusion has not been established. Therefore, in this study, which concentrates on methodological issues, we examined the characteristics of 6 different formulations of the standard [15O]water blood flow model. We estimated the reproducibility of the kinetic parameters derived from each of these formulations using data from repeated flow measurements. Finally, we examined the quantitative accuracy of the parametric images by comparing tumor blood flow values from these images with those obtained using the standard ROI methodology. These issues may prove to be particularly important in light of the development of new anticancer drugs that aim to affect tumor angiogenesis (22).
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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Data Acquisition
Image data were acquired on an Advance PET scanner (General Electric Medical Systems, Milwaukee WI) (23) that was operated in septa-extended, 2-dimensional mode. Thirty-five transaxial planes of data were acquired simultaneously with a slice-to-slice distance of 4.25 mm. Data acquisition started immediately before a peripheral intravenous injection of 1.85 GBq [15O]water that was administered as a rapid bolus over 
5 s. Each acquisition lasted for 5 min and was performed in a dynamic mode with the following frame times: 20 x 3 s, 6 x 10 s, and 6 x 30 s. To assess the reproducibility of the perfusion measurements, each patient had either 2 or 3 separate [15O]water studies. These studies were performed either on a single day or over 2 consecutive days.
All projection data were corrected for photon attenuation using data derived from an 8-min transmission scan that was acquired immediately before tracer administration. The transmission scans were acquired with septa extended using 2 rotating 68Ge rod sources that had a total activity of 333–555 MBq over the period during which the scanning was performed. The emission data were scatter corrected (24), and images were reconstructed using filtered backprojection with a transverse spatial resolution of 7-mm full width at half maximum (FWHM) at the center of the field of view. To suppress noise and thus reduce the variability of the parameter estimates in the subsequent model fitting, the images were resampled so as to have a 4 x 4 mm pixel size, and an additional smoothing filter was applied in the transaxial plane. This resulted in a spatial resolution at the center of the field of view of 14-mm FWHM in the transaxial plane and 4-mm FWHM in the axial direction.
Both MRI and FDG PET data were available for qualitative comparison with the flow images. After the last [15O]water study, the patient remained within the PET scanner and was injected with 555 MBq FDG. Forty-five minutes after injection, an additional 15-min emission scan was begun. The resulting FDG data were processed in the same way as the [15O]water data, although no additional smoothing was applied after reconstruction. T1-weighted, contrast-enhanced MR images, acquired on a 1.5-T unit (Signa; General Electric Medical Systems), were also available.
Parametric Images
[15O]Water is a chemically inert, freely diffusible tracer, and its behavior in tissue can be described by the following equation (25,26):
 | (Eq. 1) |
denotes convolution. The limited spatial resolution of the PET scanner means that measurements of tissue activity concentrations may be biased because of the partial-volume effect. In addition, the tissue activity curve may be contaminated by arterial blood from vessels nearby or within the volume of interest. To compensate for these 2 effects, one can incorporate a partial-volume factor into Equation 1 and add an additional spillover term proportional to the arterial blood activity concentration, producing the following expression:
 | (Eq. 2) |
is the corresponding recovery coefficient, and Va is the fraction of the arterial blood concentration that appears in the tissue. Note that spillover is assumed to be proportional only to the arterial activity concentration, although in certain regions venous blood may dominate and this assumption will be in error.
, f, Vd, and Va are, in general, unknown parameters to be determined by least-squares estimation. A unique solution for all 4 parameters cannot be obtained simultaneously, and this fact, plus noise constraints, means that it is necessary to reduce the number of free parameters in the fit. There are several ways to reduce the number of parameters, each of which requires slightly different assumptions. Table 1 summarizes the parameter assumptions for the 6 different formulations of the model that were considered. Model 1a derives f from the influx term ( x f) and Vd from the efflux term (f/Vd), with the assumption of perfect resolution recovery. Model 2a makes an assumption about the volume of distribution and derives f from the efflux term, which is independent of partial-volume effects. Note that models 1a and 2a are essentially the same with the flow information being obtained from different terms. Model 3a makes assumptions about the recovery coefficient and volume of distribution but calculates flow from both the influx and efflux parts of the curve. Models 1b, 2b, and 3b are identical to models 1a, 2a, and 3a but also include an arterial blood volume term that is proportional to the arterial input function. For those models in which Vd was fixed (models 2a, 2b, 3a, and 3b), we assumed a value of 0.91 mL/g, which is frequently accepted for the myocardium (21). Of course, this value may not be applicable for other tissues, and the validity of this assumption will be examined.
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2) were obtained by recursively evaluating 2 at 3 points over the k range, with the distance between each sample becoming progressively smaller. On the basis of expected flow values, the search was initially performed over the k range from 0 to 1 per minute, although if a minimum was found toward the top of this range the search was expanded to cover 0–10 per minute. A total of 2561 discrete k values were evenly sampled from 0 to 10 per minute, which, for a volume of distribution of 0.91 mL/g, resulted in flow intervals of 0.00355 mL/min/g. Fitting was performed in a weighted manner with each time frame having a weight that was inversely dependent on the variance of the image data. This variance was estimated by an approximate formula that was a function of the frame duration, scanner dead time, and the number of counts in both the prompt and delayed coincidence windows. High randoms and dead time at the start of the study, combined with short-acquisition frame times, meant that early frames were often weighted less heavily than later ones. The image dimensions were 128 x 128 and, to speed up the computation, the transmission image was used to mask out pixels that were in the surrounding air. The computation time to produce 35 slices of parametric image data for a single model was 10 min on a VAX 4000 computer (Digital Equipment Corp., Maynard, MA).
The input function Ca(t) was estimated from the image data using manually defined ROIs drawn in the left atrium. Frames 5–12 (total acquisition time, 24 s) of the dynamic water data were added to give an average image of the early phase of the study that clearly showed the blood pool. Irregularly shaped ROIs with a mean size of 4.4 ± 2.4 cm2 per slice were drawn in the left atrium in 4 adjacent planes. These ROIs were then applied to the corresponding dynamic images before the additional postreconstruction smoothing filter (and therefore at a spatial resolution of 7-mm FWHM). For each frame the mean activity concentration within the volume formed by the 4 ROIs produced an approximate, noninvasive arterial input function.
Image Analysis
The quantitative nature of the parametric images was assessed by ROI analysis. Although tumor blood flow was the main interest of the study, ROIs were drawn around regions of myocardium and soft tissue as well as tumor. The myocardium was of interest because it has been widely studied and provided an opportunity to compare the quantitative values obtained from the parametric images with previously published data. The soft-tissue regions were useful because they showed the typical flow values that might surround a tumor and they also highlighted the noise problems that occur in regions of low flow. Each ROI was manually drawn using the model 3b flow images from each patient's first water study. To compensate for patient motion between scans, the original ROIs were visually repositioned, but not redrawn, for the subsequent studies performed on the same patient. Tumors were identified in conjunction with the FDG data and ROIs (mean size, 6.5 ± 3.0 cm2 per slice) were drawn, in 3 adjacent planes, around the region of highest flow. Similarly, the myocardial ROIs (mean size, 21.1 ± 5.1 cm2 per slice) were defined in 3 transverse planes and included the septum, anterior wall, and lateral wall. The soft-tissue ROIs (mean size, 60.8 ± 24.2 cm2) were drawn in single planes and probably included a combination of pectoral muscle and fat.
The ROIs described above were applied to the parametric images for each model. The mean flow within each ROI was calculated and, in the cases of the tumor and myocardial regions, the data from multiple planes were averaged to obtain the mean flow over the volume of interest. Because an independent gold standard was not available, the mean flow values from the parametric images were compared with flows measured using the standard ROI method. The ROI method computed flow by applying the same ROIs to the dynamic water data and then fitting the resultant time–activity curves to each of the 6 models, using previously reported nonlinear regression software (27). Input functions and weights used for the ROI method were identical with those used for the pixel-by-pixel method. Therefore, the 2 methods should differ only because the mean of the individual pixel flows may not equal the flow from the mean time–activity curve from all individual pixels (especially if flow is not homogeneous throughout the ROI) and because of possible differences in the fitting algorithm.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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The tumor blood flow obtained from the parametric images compared well with the corresponding data derived from fitting the model to the regional time–activity curves (Fig. 5). Although differences in the results of the 2 approaches might be expected because of tissue heterogeneity (28), no significant differences were detected for models 1a, 1b, 2a, 2b, and 3a. The reason for this close agreement is probably associated with the fact that the image data were heavily smoothed and the pixels within the tumor regions were thus highly correlated. It may be possible to reduce the size of the transverse smoothing filter if the injected dose were increased, if additional smoothing were applied in the axial direction, or if an iterative reconstruction algorithm were used. For model 3b, the discrepancy in the flow results may be attributed to the incorrect assumptions of this particular model (i.e., that resolution recovery is perfect and that the volume of distribution is fixed at 0.91 mL/g). Including a blood term in this model provided a mechanism to artificially compensate for the differences between the measured data and the model, but the accuracy of the parameter estimates was apparently compromised. The large variability in ROI versus parametric flow values seen in Figure 5 for model 3b may be caused by the increased sensitivity of this model to the high noise levels present in the pixel-by-pixel data. Errors of this sort may be more likely to occur in regions of high flow where the tissue time–activity curve more closely resembles the input function. This problem can be visualized in the model 3b images (Figs. 1H and 2E) as a sharp discontinuity between high and low flow, which was not consistent with the 14-mm resolution of the image data. The quantitative accuracy of these images may not be reliable in these regions, but the sharp discontinuity did provide a way of identifying the high-flow part of the tumor that was used for ROI definition. Note that the invalid model assumptions described above also affect model 3a, but, because this model has only 1 free parameter, it may handle these data better. Although models 1b and 2b also include a blood volume factor, these models allow the influx and efflux terms to be independent free variables and the problem does not arise.
Although estimates of tumor blood flow obtained from the parametric images were unbiased (at least for models 1a, 1b, 2a, 2b, and 3a) with respect to the ROI method, this was not the case for other regions of the image. For nontumorous soft tissue, column 4 of Table 2 shows that the parametric images gave estimates of flow that were considerably greater than those of the ROI method, particularly for models 2a and 2b but also for models 1a and 1b. The high flow encountered in the tumors resulted in both pixel and ROI time–activity curves with relatively low noise, which meant that reasonable fits were achieved. For other parts of the body, the blood flow was lower and the time–activity curves, particularly for the parametric method, were much noisier. This led to model parameters with relatively high variance, especially in the case of models 1a, 1b, 2a, and 2b, which had 2 or 3 free parameters. In our implementation of the parametric method, model parameters were always computed, although noisy data tended to produce k values (14) toward the maximum of the permitted search range (these points are readily apparent in Figs. 1E and F). Even when the search algorithm was replaced by a brute-force search that examined all k values in the permitted range, the problem remained. This effect is equivalent to a failure to converge (when the influx is low it is difficult to measure the efflux) and accounts for the very high flow values encountered in the soft-tissue regions of the parametric images (for models 1a, 1b, 2a, and 2b).
For the soft-tissue data obtained with models 3a and 3b, good agreement can be seen between the ROI and parametric imaging results (Table 2). This is because these models imposed a more constrained fit and, in all cases, reached convergence. Although these ROIs probably contain a mixture of muscle, fat, and other soft tissue, the flow values agree well with previously reported muscle blood flow values of 0.018 ± 0.010 mL/min/g (29). The flow values obtained with the ROI method for models 1a and 1b are also consistent with these previously published values, but the flow values for models 2a and 2b are an order of magnitude greater. This is associated with the fact that, in these models, an assumption was made about the volume of distribution. The flow information comes entirely from the washout term and, although this value is expected to be largely independent of partial-volume effects, it requires that the volume of distribution be known. For the myocardium, this value is thought to be 0.91 mL/g, but it is not likely that this value is applicable throughout the body. From model 1b we can estimate the volume of distribution, and the data in Table 3 show a value of 0.123 ± 0.039 mL/g (ROI method) for soft tissue. Taking Vd = 0.91 mL/g was therefore a poor approximation, in this case, and might account for the errors in the soft-tissue flow data obtained with these models. For the tumor regions, the volume of distribution was found to be 0.80 ± 0.15 mL/g and 0.79 ± 0.14 mL/g for the parametric image and ROI methods, respectively. These values may be underestimates (30) of the true values because of partial-volume effects, and it seems that the assumed value of 0.91 mL/g might be more accurate for these tumors than for soft tissue. Of course, other tumors may have quite different volumes of distribution, in which case models that do not fit Vd would be incorrect. Further studies involving a larger group of tumors would be required to verify this.
In one of the few quantitative studies of tumor blood flow (11), values of flow in malignant lesions were found to be 0.298 ± 0.170 mL/min/g. This study was of breast tumors, and flow was calculated using the model that we have referred to as model 1a. At least 2 of the 5 patients in our study had values of tumor blood flow that were significantly greater than this value: approximately 4.2 and 3.6 mL/min/g. Although these values seem surprisingly high, it should be remembered that renal cell metastases are known to be very vascular tumors. In addition, the flow in other parts of these images was in the normal range, suggesting that the high-flow values for tumor are reliable. The mean myocardial blood flow for all 5 patients, obtained with model 2b (the model typically used for cardiac studies) was 1.18 ± 0.13 and 1.09 ± 0.15 mL/min/g for the parametric and ROI methods, respectively. All 5 patients were expected to have normal myocardial flow, and our data, including the 2 patients with the high tumor flows, were consistent with previously reported normal values of 0.95 ± 0.09 mL/min/g (21), obtained using the same model. The pixel-by-pixel method overestimated flow by 8.5% ± 2.8% compared with the ROI method. This is not unexpected. The pixels near the edge of the myocardium had very low counts and resulted in flow values that had large relative SDs. Because the lowest possible flow value was 0 and the highest was (arbitrarily) 10, averaging such noisy pixel values together would bias the flow data to slightly high values. This effect does not occur with the ROI method because the pixels with the low counts do not contribute significantly to the mean time–activity curve.
In this study, the parts of the body that could be investigated were restricted by the limited axial extent of the PET scanner and the requirement to have the heart in the field of view. This enabled the input function to be obtained from the image data and meant that the entire procedure could be performed in a noninvasive manner, without arterial blood sampling (31,32). Quantitative errors in determining the arterial input function may arise because of partial-volume and spillover problems, but these were expected to be small because of the large blood pool in the left atrium and the relatively low spillover from [15O]water in the atrial walls. Extending the parametric imaging approach to other parts of the body would require more sophisticated techniques for extracting the input function from images (33).
More complex kinetic models may be required in certain circumstances (e.g., liver (34)) but, even in these cases, the simple method we present may be useful to help visualize regional differences in blood flow. It is unlikely that any single model will be completely valid for all parts of the body, and this should be borne in mind when interpreting parametric images. Highly accurate quantification may not always be possible using simple models such as model 3a. Nonetheless, the parametric images generated in this way are useful to aid the placement of ROIs (without the need for registration with complementary images), to permit detailed regional analysis, and to assess potential inhomogeneities in flow over the tumor.
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CONCLUSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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For correspondence or reprints contact: Stephen L. Bacharach, PhD, Rm. 1C401, Bldg. 10, National Institutes of Health, Bethesda, MD 20892-1180.
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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  M. A. Lodge, H. A. Jacene, R. Pili, and R. L. Wahl Reproducibility of Tumor Blood Flow Quantification with 15O-Water PET J. Nucl. Med., October 1, 2008; 49(10): 1620 - 1627. [Abstract] [Full Text] [PDF]
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