Quantification of myocardial blood flow with 82Rb: Validation with 15O-water using time-of-flight and point-spread-function modeling
© The Author(s). 2016
Received: 11 March 2016
Accepted: 30 June 2016
Published: 1 August 2016
We quantified myocardial blood flow with 82Rb PET using parameters of the generalized Renkin-Crone model estimated from 82Rb and 15O-water images reconstructed with time-of-flight and point spread function modeling. Previous estimates of rubidium extraction have used older-generation scanners without time-of-flight or point spread function modeling. We validated image-derived input functions with continuously collected arterial samples.
Nine healthy subjects were scanned at rest and under pharmacological stress on the Siemens Biograph mCT with 82Rb and 15O-water PET, undergoing arterial blood sampling with each scan. Image-derived input functions were estimated from the left ventricle cavity and corrected with tracer-specific population-based scale factors determined from arterial data. Kinetic parametric images were generated from the dynamic PET images by fitting the one-tissue compartment model to each voxel’s time activity curve. Mean myocardial blood flow was determined from each subject’s 15O-water k 2 images. The parameters of the generalized Renkin-Crone model were estimated from these water-based flows and mean myocardial 82Rb K 1 estimates.
Image-derived input functions showed improved agreement with arterial measurements after a scale correction. The Renkin-Crone model fit (a = 0.77, b = 0.39) was similar to those previously published, though b was lower.
We have presented parameter estimates for the generalized Renkin-Crone model of extraction for 82Rb PET using human 82Rb and 15O-water PET from high-resolution images using a state-of-the-art time-of-flight-capable scanner. These results provide a state-of-the-art methodology for myocardial blood flow measurement with 82Rb PET.
Cardiac perfusion PET with 82Rb is clinically useful for diagnosing coronary artery disease [1–4]. Quantification of myocardial blood flow (MBF) and coronary flow reserve (CFR) can be obtained from 82Rb PET but relies on accurately modeling the extraction fraction of rubidium by myocardial tissue, which is nonlinearly related to flow as described by the generalized Renkin-Crone model [5–8]. Uncertainty in the extraction model parameters causes much of the uncertainty in MBF .
Several groups have reported generalized Renkin-Crone model parameters for rubidium using canine or human MBF data from microspheres , 13N-ammonia [5, 11], and 15O-water [12, 13]. Most of these studies used older-generation PET systems with 2D or reduced-dose 3D acquisitions. To our knowledge, no extraction fraction estimations have been made using scanners with time-of-flight (TOF) capabilities; for 82Rb PET, such systems provide better signal-to-noise ratios than non-TOF systems [14, 15] and parametric images with lower standard error. Further, when point spread function (PSF) modeling is included in reconstruction, MBF estimates from 82Rb PET may be higher ; however, such calculations were performed using an extraction model  derived from non-TOF, non-PSF images. Presotto et al.  demonstrated the quantitative superiority of PSF + TOF for dynamic cardiac reconstructions using a thorax/heart phantom filled with either 18F alone or 18F and 13N (to simulate dynamically varying contrast), in both static and moving configurations.
Errors in the input function, another critical component of kinetic modeling, can substantially bias kinetic parameter estimates . For practical reasons, image-derived input functions (IDIFs) are widely used in cardiac PET. IDIFs estimated from blood pool regions of cardiac images have been validated against the gold standard of arterial samples in dogs [5, 19] but not recently in humans with 82Rb PET.
A recent study of five extraction model fits and three IDIF estimation methods demonstrated that these choices substantially influence MBF estimates . In this work, we reexamined extraction fraction estimation in humans with paired rest and stress studies with 82Rb and 15O-water acquired on a state-of-the-art system, the Siemens Biograph mCT, and reconstructed images with TOF and PSF modeling. We augmented this high-quality image data with continuously sampled arterial measurements for input function validation. From these data, we provided new parameter estimates of the generalized Renkin-Crone model for rubidium extraction.
Nine healthy subjects (five male) with no known cardiac abnormalities were studied. This study was approved by the Yale University Human Investigation Committee; all subjects signed an informed consent form. The average age was 28.4 ± 6.2 years, and average BMI was 24.7 ± 3.9 kg/m2. Subjects abstained from caffeine for 12 h pre-imaging, and from food for 4–6 h. Before scanning, an intravenous line for tracer administration and an arterial line for blood sampling were placed.
PET scans were acquired on the Biograph mCT 1104 (Siemens Healthcare, Knoxville, TN) at rest and under pharmacological stress with 82Rb and 15O-water for each subject. For seven subjects, the scan sequence was: 82Rb rest; 15O-water rest; 15O-water stress; and 82Rb stress. For the remaining subjects, the 82Rb stress acquisition was performed directly after the 82Rb rest acquisition. A 1-h interval separated each stress scan from the following acquisition, with confirmation that heart rate and blood pressure had returned to baseline. Low-dose CT attenuation correction scans were acquired before each rest scan and after each stress scan. Pharmacological stress was induced with 0.4 mg of regadenoson, injected over 30 s, 1 min before tracer injection. The 82Rb injections were performed with the CardioGen-82 (Bracco Diagnostics, Princeton, NJ) system with an infusion rate of 50 mL/min, duration of 18 ± 4 s, and mean ± SD dose of 663 ± 82 MBq. 15O-water infusions with mean dose 690 ± 136 MBq were delivered over 20 s. Dosing was independent of body weight.
Arterial blood sampling and data analysis
Arterial blood was drawn from the radial artery for 7 min per scan at 4 mL per minute for seven of nine subjects and radioactivity measured with a cross-calibrated radioactivity monitor (PBS-101, Veenstra Instruments, Joure, The Netherlands). One subject chose not to have the arterial line. In another subject, the arterial line was not successfully placed. Because IDIFs were corrected with population-based scale factors, these subjects’ image data were not excluded. Because the 1.25-mL infusion line for 82Rb was not flushed, residual activity remained at end-of-elution. This unshielded activity contributed to the background signal detected by the radioactivity monitor, visible in the initial portion of the 82Rb arterial readings before the input function peak (when measurements should be 0). To model this background signal, a decaying exponential with the 82Rb decay constant was fit to the raw count data for each acquisition, between end-of-elution and the rise of the input function peak. This fitted curve was subtracted from the arterial measurements (see Additional file 1, page 1). Apart from removal of the background signal, 82Rb and 15O-water data were processed analogously. Corrections were applied for sensitivity, decay, and external dispersion. Sensitivity was measured by cross-calibration with phantom measurements per isotope. To correct for time delay between the left ventricle (LV) and the arterial sampling site, each acquisition’s time shift was estimated by maximizing the correlation between the corrected arterial samples and the LV time activity curve (TAC).
For each injection, list-mode data were acquired for 4 min post-injection and reconstructed into 32 frames (20x3s,6x10s,6x20s) with mCT software using TOF and PSF modeling, and, for 82Rb, prompt-gamma correction (OSEM with 2 iterations of 21 subsets, voxel size 2.036x2.036x2.0 mm3). Images were post-smoothed with a 3 mm-FWHM Gaussian kernel. Summed dynamic PET images were inspected for alignment with the corresponding attenuation correction CT images, and manually realigned and re-reconstructed as necessary. Images were transformed to short-axis orientation.
Input function estimation
IDIFs were estimated from fixed-volume (6.5 mL) cylindrical VOIs manually placed towards the base of the LV and atrium blood pools of each image (Fig. 1b). The resulting TACs were compared to the measured arterial input functions (AIFs) with regard to peak concentration, tail concentration, and area under the curve (AUC). For comparisons, AIFs were resampled to the image times by averaging values within each frame. Peaks were computed as the maximal activity of each TAC. Tail activity was computed as the average concentration over 1 min starting at 2 min, 40 s post-injection. Percent difference in each metric was computed for corresponding pairs of IDIFs and AIFs and averaged across subjects.
With a sufficiently small LV VOI, activity is often assumed to be fully recovered [10–12]; alternatively, IDIFs are sometimes corrected for partial-volume effects. For instance,  assumed the LV cavity TAC is a partial-volume mixture of 85 % arterial blood and 15 % myocardial tissue. We investigated partial-volume correction (PVC) methods using the AIF as the gold standard.
The sum β1 + β2 might be <1 if partial-volume mixing occurs with signal outside the heart (e.g., the lung).
This correction was used by , with tracer-independent β s ≈ 0.90 estimated from canine 82Rb and 13N-ammonia PET and well counter measurements of arterial samples.
where T is the duration of the dynamic acquisition. While individually estimated β AUC cannot outperform β s in terms of weighted sum-of-squared residuals (WSS) (β s minimizes WSS by design), a population-based β AUC might give better kinetic parameter concordance.
Parameters for the one-parameter PVC, two-parameter PVC, and scaling models (Eq. 3, 4, and 5, respectively) were estimated via WLS for each acquisition. Model fits were compared by F tests. The 82Rb K 1 estimates and 15O-water k 2 estimates from AIFs were compared to those from β AUC scale-corrected IDIFs by linear Deming regression, which models error in both variables, and by the Lin concordance coefficient , which provides a measure of absolute agreement between two estimates.
Comparison of uncorrected IDIFs to AIFs
% difference mean ± SD
% difference mean ± SD
% difference mean ± SD
−11 ± 12
−13 ± 9.2
−7.1 ± 18
−6.0 ± 13
−19 ± 18
2.6 ± 23
−5.1 ± 10
−8.4 ± 14
−5.4 ± 9.0
−1.2 ± 9.9
2.4 ± 18
−3.5 ± 7.8
Using the two-parameter PVC method, the mean and standard deviation of β 1 + β 2 (Eq. 4) were 0.85 ± 0.10 (0.98 ± 0.10) for 82Rb (15O-water). This indicates that while a partial-volume mixture model of arterial blood and myocardium tissue may be sufficient for water, rubidium could require a different model of recovery-diminishing effects.
The mean and standard deviation of the scaling parameter β s (Eq. 5) was 0.83 ± 0.09 (0.94 ± 0.10) for 82Rb (15O-water). The scaling parameter β AUC (Eq. 6) was 0.92 ± 0.12 (0.97 ± 0.10) for 82Rb (15O-water). Additional file 1: Table S1 gives mean estimated correction parameters by tracer and condition.
Additional file 1: Figure S3 gives results of F-tests comparing the two-parameter PVC model to either the one-parameter PVC or scaling model (Eq. 5) for each acquisition. For 11 of 14 82Rb scans, the two-parameter PVC model outperformed the one-parameter PVC model. For only four 82Rb scans, the two-parameter model outperformed scaling with β s. For most 15O-water acquisitions, the two-parameter model was not superior to either one-parameter model (Eqs. 3 and 5).
The AUC scale correction (Eq. 6) cannot be compared to scaling with β s by F-test, since the WSS of the AUC scale correction will always be at least that of the β s correction. With the β s correction, the difference in IDIF peak compared to AIF peak was 1 ± 17 % (3 ± 17 %) for 82Rb (15O-water); the difference in AUC becomes 10 ± 15 % (3 ± 10 %) for 82Rb (15O-water). With the β AUC correction, the difference in peaks becomes −9 ± 16 % (0 ± 17 %) for 82Rb (15O-water); the difference in AUC becomes 0 ± 13 % (0 ± 10 %) for 82Rb (15O-water). Though β s correction provides better peak agreement, β AUC correction improves the peak agreement while also improving AUC agreement.
Based on these results, AUC-based scaling correction was adopted. All IDIFs were corrected by multiplication with the reciprocal of the average β AUC per tracer (1.09 for 82Rb, 1.03 for 15O-water). Eleven of 14 82Rb and 10 of 14 15O-water IDIFs had better agreement (lower WSS) with the AIF after scaling, with an average decrease in WSS of 18 ± 23 and 3 ± 16 %, respectively.
For this subject, the 82Rb K 1 images from corrected IDIFs showed qualitatively better agreement with those from AIFs than those using uncorrected IDIFs (Fig. 4a). Because corrected IDIFs were generated using a population-based correction factor, not all scans had comparable improvement in agreement between corrected IDIF- and AIF-based images. The IDIF correction factor was closer to unity for 15O-water than 82Rb, so 15O-water K 1 images were less affected by IDIF correction. The IDIF correction had virtually no impact on k 2 parametric images (Fig. 4b), as K 1 and V A compensate changes in input function scale.
Mean kinetic parameter estimates from three-parameter fit (without V RV)
K 1 (mL/min/g) mean ± SD
0.43 ± 0.09
0.45 ± 0.05
0.53 ± 0.06
0.87 ± 0.21
0.86 ± 0.15
0.91 ± 0.16
0.99 ± 0.19
1.11 ± 0.13
1.30 ± 0.17
3.43 ± 1.62
3.53 ± 0.85
3.68 ± 0.89
k 2 (1/min) mean ± SD
0.11 ± 0.05
0.13 ± 0.04
0.13 ± 0.04
1.10 ± 0.31
1.05 ± 0.22
1.05 ± 0.22
0.21 ± 0.06
0.23 ± 0.08
0.23 ± 0.08
3.76 ± 1.24
4.10 ± 1.06
4.10 ± 1.06
V A mean ± SD
0.32 ± 0.05
0.37 ± 0.04
0.40 ± 0.05
0.29 ± 0.08
0.33 ± 0.05
0.34 ± 0.06
0.31 ± 0.06
0.40 ± 0.06
0.44 ± 0.06
0.27 ± 0.06
0.27 ± 0.06
0.28 ± 0.06
This study’s mean 82Rb rest and stress K 1 and k 2 estimates using scaled IDIFs were comparable to those reported by . The V A estimates were approximately 20 % lower than those in , likely attributable to IDIF correction and the improved resolution of this study’s images.
Extraction fraction parameter estimates
Renkin-Crone parameter estimates from this and published studies
Renkin-Crone parameter estimates
Input function correction
a ± SE
b ± SE
0.74 ± 0.03
0.51 ± 0.09
0.77 ± 0.03
0.39 ± 0.06
Yoshida 1996 
0.85 ± 0.03
0.45 ± 0.08
Lortie 2007 
0.77 ± 0.05
0.63 ± 0.17
Lautamaki 2009 
Prior 2012 
0.80 ± 0.04
0.59 ± 0.14
Katoh 2012 
2-parameter partial-volume correction
Renaud 2013 
Extraction-corrected population estimates of myocardial blood flow, mean (±standard deviation)
82Rb MBF (mL/min/g)
15O-water MBF (mL/min/g)
0.92 ± 0.19
0.96 ± 0.20
3.65 ± 0.64
3.73 ± 0.96
0.91 ± 0.19
0.96 ± 0.20
3.59 ± 0.55
3.73 ± 0.96
This study estimated Renkin-Crone extraction model parameters for rubidium using state-of-the-art 82Rb and 15O-water TOF PET images with PSF reconstruction. IDIF estimation was validated with continuously sampled arterial blood measurements (AIFs).
Armstrong et al.  provided a comparison of reconstructions with TOF and PSF to standard reconstructions; they reported an average increase in MBF of 10–14 % in advanced reconstructions compared to standard OSEM, which is consistent with improved recovery of signal in the myocardium. Because that study used only 82Rb, extraction could not be estimated from the advanced reconstructions.
The PSF modeling used here was not isotope-specific. Because 15O and 82Rb have poorer resolution than 18F, the PSF modeling will provide only partial resolution recovery. Though the employed reconstruction should provide better resolution than reconstruction without PSF modeling, there is further room for improvement.
Resolution modeling in PET reconstruction can produce ringing artifacts that significantly impact quantification . These effects are most often detectible in simulation and phantom studies with well-defined object borders. Here, because of the additional blurring incurred by uncompensated cardiac and respiratory motion and modest Gaussian filtering applied pre-modeling, Gibbs-like artifacts were not observed.
While PSF modeling and TOF can provide improved resolution, the primary benefit in this application is reduced noise in the parametric images. For representative maps of the standard error of 82Rb K 1 and 15O-water k 2, see Additional file 1: Figure S9.
In 3D PET with high injected activities, inaccurate corrections for detector deadtime can impact the accuracy of reconstructed activity in early frames. A previous patient study on the Biograph mCT suggests that doses of 82Rb <1110 MBq can avoid significant detector saturation . The doses used in the present study were on average ~60 % of this, and none exceeded it. Based on the peak singles rates, the average peak deadtime was 35 ± 8 % (32 ± 7 %) for 82Rb (15O-water).
PET image resolution is affected by positron range, detector resolution, smoothing in the reconstruction, and motion. Poor resolution affects quantification of myocardial activity and IDIFs. To minimize the impact of these effects on IDIFs, VOIs are typically small and central in the blood cavity where spill-in and spill-out are presumed insignificant. IDIF accuracy is important to kinetic modeling results; simulations show that a 10 % error in the IF peak can bias 82Rb K 1 estimates by up to 25 % . Thus, verification of IDIF accuracy is highly important.
IDIFs had lower correspondence with AIFs for rubidium than water, particularly in terms of peak activity. Unlike water, rubidium is retained in myocardial tissue, causing the tail of the blood pool TAC to fall below that of the myocardium TAC (water IDIFs will have matched activity in the tails of the LV cavity and myocardium TACs). When 82Rb images are degraded by motion and resolution effects, expected consequences for IDIFs are reduced peak activity (spill-out from LV cavity) and increased tail activity (spill-in from myocardium). Though prior publications’ images [11, 12] were likely of poorer resolution than this study’s, their IDIFs were uncorrected. In the current study, we primarily observed reduced peak activity in 82Rb IDIFs, with differences in tail activity inconsistent with a strict model of geometric PVC (Eq. 3). In Katoh et al. , LV TACs were corrected using a PVC model; that model overcorrected the tails of our 82Rb IDIFs. A mismatch between 82Rb IDIFs and AIFs was better described using a two-parameter model (Eq. 4), which provides for signal mixing with background regions. The simpler scale factor correction (Eq. 5), which recovers activity from an unspecified combination of resolution degradation effects, gave comparable results. For half the 82Rb acquisitions, the AUC-based scale factor β AUC (Eq. 6) was approximately equal to the scan-specific β s (Eq. 5). For the rest, β AUC was markedly higher than β s; in these cases, the IDIF more greatly underestimated the AIF peak, with lower error in the tail. When β s is used to correct these cases, though the average peak error is reduced to ~0, the average AUC is overestimated, because tail activity is overestimated.
We chose scaling IDIFs based on AUC matching as more appropriate than WLS-based scaling. For 15O-water, the differences between the two methods were small. 82Rb, however, is more sensitive to the input function AUC, as its uptake is approximately irreversible. For such tracers, tissue activity is directly proportional to the input function AUC, so errors in the AUC propagate into the parameter estimates.
Given our AIF measurements and anticipating that population-based IDIF correction is most practical for scans without arterial sampling, we used mean tracer-dependent scale factors to correct IDIFs. However, the optimal correction factor is scan-dependent, conditional on variations in VOI size and placement, heart size, breathing pattern, and subject motion. Further investigation is required to assess generalizability to other scanners and reconstruction algorithms. Using AIFs for modeling does not guarantee accurate parameter estimates, as error in myocardial TACs not addressed by the partial-volume fractions V A and V RV (Eq. 2) could induce bias. Body and respiratory motion are likely principal sources of error. One limitation this study shares with previous publications is that no motion compensation was incorporated.
The Renkin-Crone model fits obtained in this study are similar to previously published fits, though our b estimate is lower, primarily a reflection of lower 82Rb K 1 estimates in this study compared to others, from the IDIF correction that was applied. With uncorrected IDIFs, extraction parameters obtained in this study closely match those previously published by Lortie . Because scaling correction impacts 82Rb K 1 but not 15O-water k 2, scaled IDIFs resulted in a decrease in the b parameter of the Renkin-Crone model. For most previous studies, there was no gold standard measurement of the input function, and therefore, no basis for IDIF correction. Katoh et al.  used partial-volume corrected IDIFs, which explains the better agreement between their extraction model and that from corrected IDIFs in this study, compared to the Lortie model. The a parameter of the Renkin-Crone model is less sensitive to IDIF correction and reported values vary less across the literature.
Some differences in Renkin-Crone fits can also be explained by the flow estimation method. For instance,  used 13N-ammonia to measure MBF, which has a lower extraction fraction than 15O-water and will hence underestimate MBF. Using unweighted ODR to fit the data instead of weighted ODR resulted in higher parameter estimates (Additional file 1: Figure S10). Average MBFs were similar regardless of IDIF correction because water-based flows were unaffected by IDIF scaling and extraction parameters were estimated separately for each case. Therefore, accurate flows can be determined for 82Rb with or without IDIF correction, if extraction parameters have been estimated from data processed similarly. This suggests that modeling choices could have greater impact on extraction fraction estimates than TOF and PSF modeling, though TOF/PSF-based kinetic parameters have lower standard error.
We have presented parameter estimates for the generalized Renkin-Crone model of extraction for 82Rb PET using human 82Rb and 15O-water PET from high-resolution images from a state-of-the-art TOF-capable scanner with PSF reconstruction. The image-derived input functions were validated against direct arterial measurements, and a scale correction improved the accuracy of IDIFs. With this IDIF correction, MBF should be estimated from 82Rb K 1 using the Renkin-Crone parameters reported here. These results provide a state-of-the-art methodology for MBF measurement with 82Rb PET, though further validation will be necessary in patients with coronary artery disease with infarcts and ischemia.
AIF, arterial input function; IDIF, image-derived input function; LV, left ventricle; MBF, myocardial blood flow; PSF, point spread function; PVC, partial-volume correction; RPP, rate-pressure product; RV, right ventricle; TAC, time activity curve; TOF, time-of-flight; VOI, volume of interest; WLS, weighted least squares
This work was supported by Siemens Medical Solutions and NIH grants 1S10OD010322-01 and 1F31EB018720-01. This publication was made possible by CTSA Grant Number UL1 TR000142 from the National Center for Advancing Translational Science (NCATS), a component of the National Institutes of Health (NIH). Its contents are solely the responsibility of the authors and do not necessarily represent the official view of NIH.
Availability of data and materials
The data supporting the conclusions of this article are included within the article (and its additional files).
JR and NN performed synthesis of 15O-water. CL, AS, RC, EA, and HF designed the imaging protocol and assisted in image acquisition. MG, TM, and KF performed data processing and analysis. MG, RC, AS, KF, CL, and TM prepared the manuscript. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
Consent for publication
Ethics approval and consent to participate
All procedures performed in studies involving human participants were in accordance with the ethical standards of the Yale University Human Investigation Committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. All participants signed a consent form.
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