- Original research
- Open Access
FDG kinetic modeling in small rodent brain PET: optimization of data acquisition and analysis
- Malte F Alf^{1},
- Marianne I Martić-Kehl^{2},
- Roger Schibli^{1} and
- Stefanie D Krämer^{1}Email author
- Received: 14 April 2013
- Accepted: 25 July 2013
- Published: 6 August 2013
Abstract
Background
Kinetic modeling of brain glucose metabolism in small rodents from positron emission tomography (PET) data using 2-deoxy-2-[^{18} F]fluoro-d-glucose (FDG) has been highly inconsistent, due to different modeling parameter settings and underestimation of the impact of methodological flaws in experimentation. This article aims to contribute toward improved experimental standards. As solutions for arterial input function (IF) acquisition of satisfactory quality are becoming available for small rodents, reliable two-tissue compartment modeling and the determination of transport and phosphorylation rate constants of FDG in rodent brain are within reach.
Methods
Data from mouse brain FDG PET with IFs determined with a coincidence counter on an arterio-venous shunt were analyzed with the two-tissue compartment model. We assessed the influence of several factors on the modeling results: the value for the fractional blood volume in tissue, precision of timing and calibration, smoothing of data, correction for blood cell uptake of FDG, and protocol for FDG administration. Kinetic modeling with experimental and simulated data was performed under systematic variation of these parameters.
Results
Blood volume fitting was unreliable and affected the estimation of rate constants. Even small sample timing errors of a few seconds lead to significant deviations of the fit parameters. Data smoothing did not increase model fit precision. Accurate correction for the kinetics of blood cell uptake of FDG rather than constant scaling of the blood time-activity curve is mandatory for kinetic modeling. FDG infusion over 4 to 5 min instead of bolus injection revealed well-defined experimental input functions and allowed for longer blood sampling intervals at similar fit precisions in simulations.
Conclusions
FDG infusion over a few minutes instead of bolus injection allows for longer blood sampling intervals in kinetic modeling with the two-tissue compartment model at a similar precision of fit parameters. The fractional blood volume in the tissue of interest should be entered as a fixed value and kinetics of blood cell uptake of FDG should be included in the model. Data smoothing does not improve the results, and timing errors should be avoided by precise temporal matching of blood and tissue time-activity curves and by replacing manual with automated blood sampling.
Keywords
- CMR_{glc}
- FDG
- Fractional blood volume
- Kinetic modeling
- Reliability
- Positron emission tomography
- Infusion
Background
Literature results of two-tissue compartmental FDG kinetic modeling in small rodents
Reference | K _{1} | k _{2} | k _{3} | k _{4} | K _{FDG}(mL/min/cm ^{3}) | v _{b}(%) | CMR _{glc}(μmol/min/100 g) | Anesthesia | LC | Sp |
---|---|---|---|---|---|---|---|---|---|---|
Millet et al. [12] | 0.14 ± 0.05 | 0.19 ± 0.25 | 0.07 ± 0.05 | 0.005 ± 0.004 | 0.044 ± 0.013 | -^{a} | 90.3 ± 27.6 | Urethane | 0.6 | R |
Wu et al. [14] | 0.10 ± 0.03 | 0.21 ± 0.10 | 0.05 ± 0.02 | 0.015 ± 0.006 | 0.019 ± 0.005 | 0 | 21.5 ± 4.3 | Isoflurane | 0.625 | M |
Yu et al. [15] | 0.22 ± 0.05 | 0.48 ± 0.09 | 0.06 ± 0.02 | 0.025 ± 0.010 | 0.024 ± 0.007 | 0 | 40.6 ± 13.3 | Isoflurane | 0.6 | M |
Mizuma et al. [13] | 0.20 ± 0.02 | 0.39 ± 0.05 | 0.14 ± 0.02 | 0.015 ± 0.002 | 0.053 ± 0.013 | 0 | 39 ± 3 | Awake | 0.625 | M |
Mizuma et al. [13] | 0.156 ± 0.009 | 0.329 ± 0.005 | 0.032 ± 0.006 | 0.009 ± 0.004 | 0.014 ± 0.004 | 0 | 13 ± 4 | Isoflurane | 0.625 | M |
Alf et al. [7] | 0.27 ± 0.09 | 0.57 ± 0.10 | 0.08 ± 0.02 | 0.018 ± 0.004 | 0.035 ± 0.013 | 5.5 | 61 ± 11 | Isoflurane | 0.6 | M |
We have recently introduced an FDG infusion protocol for kinetic modeling in mice [7]. The purpose of administering FDG over several minutes by a constant infusion rate rather than by a rapid bolus was to overcome the problem of inhomogeneous distribution in the blood pool after rapid injection and to allow for longer time intervals in the recording of radioactivity in blood and tissue of interest. In this recent study, we made an assumption for v _{b} based on computed tomography measurements [16]. Here, we address the question whether v _{b} can be reliably fitted from the IF, TAC, and blood time-activity curve in mouse brain FDG kinetic modeling under the applied experimental conditions. In parallel, we investigate the influence of data smoothing and time delays between IF and TAC. In a next step, we assess the influence of different IF corrections for FDG uptake into blood cells. Finally, we evaluate by simulations whether our infusion protocol indeed tolerates lower sampling frequency of blood than bolus injection. This could be of advantage for manual blood sampling or the generation of image-derived IFs, in particular in longitudinal studies where shunt surgery for high-frequency blood sampling is not feasible. Based on our findings, we suggest some guidelines for mouse brain FDG kinetic modeling.
Methods
Data acquisition and kinetic modeling
We used experimental TACs and blood-activity curves from a previous study [7] with C57BL/6 mice (n = 5) with normal glycemia (plasma glucose 11.9 ± 4.0 mmol/L (6.7 to 16.9 mmol/L)) for our analysis. In brief, animals were under isoflurane (1.5% to 2%) anesthesia, and body temperature and respiratory frequency were controlled at 36°C to 37°C and approximately 90 cycles/min, respectively. FDG (10 to 14 MBq) was administered intravenously as a constant infusion over 4.0 to 5.3 min. Blood radioactivity was recorded with a coincidence counter (Twilite, Swisstrace GmbH, Zurich, Switzerland) on a shunt volume of approximately 60 μL with 1-s temporal resolution. List mode data were acquired for 45 min on a GE Healthcare/Sedecal (Madrid, Spain) eXplore VISTA PET/CT scanner in parallel.
Calibration of the coincidence counter with respect to the PET scanner was performed daily. A syringe containing approximately 1 MBq/cm^{3} FDG solution was attached to a catheter as used for the shunt [7], and FDG solution was flushed through the catheter which was guided through the coincidence counter. The syringe and catheter were measured simultaneously with scanner and coincidence counter, respectively. FDG radioactivity (Bq/cm^{3}) was calculated from the images of the calibrated scanner and divided by the coincidence counts per cubic centimeter from the blood counter. This ratio was used to calculate blood radioactivity in the animal experiments.
Image data were reconstructed into 33 to 39 time frames with the shortest frames (10 s) around the infusion stop and longer frames toward the end of the scan (maximal length 240 s) and analyzed with PMOD v3.4 (PMOD Technologies Inc., Zurich, Switzerland). TACs were derived from the cortex and hypothalamus, respectively, with anatomic templates of PMOD covering the entire structures. Figure 1B shows experimental TACs and IF of one representative experiment.
where n is the total number of observations (O _{i}) and E _{i} is the expected value for O _{i} as calculated with the fit function.
Influence of choice of fractional blood volume on fit parameters
The effect of different assumptions for v _{b} on the fitted model parameters and χ^{2} for the cortex and hypothalamus was tested by systematically varying v _{b} between 0 and 0.2 (i.e., 0% and 20% blood in tissue, in steps of 0.5%). Alternatively, v _{b} was included as a variable parameter in the fit. In order to reduce the impact of noise in the experimental data on χ^{2}, smoothed TACs and IFs were generated from the whole experimental datasets with robust locally weighted regression (LOWESS) smoothing as implemented in MATLAB. Furthermore, to assess the effects of limited degrees of freedom, every second data point was deleted from the experimental TACs. Modeling was then performed as described above with fixed or variable v _{b} for each of the five scans with the following five combinations: unmodified experimental IF with unmodified TAC or with TAC after deletion of every second data point or with smoothed TAC, as well as smoothed IF with unmodified TAC or with smoothed TAC. To visualize the effect of the chosen v _{b} on CMR_{glc}, CMR_{glc} values were normalized to the averaged CMR_{glc} over all v _{b} for each scan (CMR_{glc} at a particular v _{b}/averaged value of all calculated CMR_{glc} of this scan) and plotted against v _{b}. For the rate constants K _{1} to k _{4}, average values from the five scans were plotted against v _{b}.
Influence of time delays between IF and TAC and of miscalibration between scanner and coincidence counter
To estimate the effect of time delays between TAC and IF, we shifted the experimental unmodified IF relative to the experimental unmodified TAC within a window of −20 to 30 s and plotted χ^{2} of the model fits (with constant v _{b} 0.055) against the timing error. To visualize the influence on CMR_{glc} and the single rate constants, the parameters were normalized to the respective value at zero time delay for each scan (e.g., CMR_{glc} (delay i)/CMR_{glc} (no delay)). To simulate a minor miscalibration by 5% between scanner and coincidence counter, the TAC was multiplied with 0.95 and 1.05, respectively. The resulting model fit parameters were compared to correctly time-matched and calibrated data fitting results.
Fit of the IFs and simulations of IFs of a bolus and two infusion protocols
Note that A, B, and Z are proportional to the infusion rate. A, B, Z and α, β, ζ were fit from the experimental IFs and kinetic analysis of the PET data was performed as described above with the fitted IF function. Fit FDG rate constants were compared to those with experimental IFs.
Simulation of TACs and FDG kinetic modeling with different infusion protocols
IFs with bolus/infusion durations of 10 s (bolus), 300 s (similar to our experimental infusion protocol), and 900 s (for comparison) were simulated from the fit parameters A, B, Z, α, β, ζ with Equations 6 and 7 after adjusting A, B, and Z to the respective infusion rate (at equal FDG dose as in the experiment). The corresponding TACs were simulated with the PMOD software, applying the FDG two-tissue compartment model and K _{1}, k _{2}, k _{3}, k _{4} from the fits with the experimental IFs and TACs with v _{b} 0.055. The number and minimal/maximal lengths of time frames for the simulated TACs were equal to the experimental data; however, shortest time frames were grouped around the corresponding injection/infusion stop. Blood radioactivities required for the correction with v _{b} were simulated from the generated IF according to Equation 3.
Once IFs and TACs were generated, Gaussian noise was added with the Excel function NORMINV to the simulated data. The standard deviation for noise generation of the IF consisted of a constant between 25 and 40 kBq/cm^{3} plus 4% to 6% of the simulated plasma concentration. For TAC simulations, a relative standard deviation was chosen for the Gaussian noise corresponding to the simulated TAC value multiplied with 0.8 and divided by the lengths of the time interval in seconds. These standard deviations yielded similar noise levels as observed for the experimental data. For each animal and infusion protocol, one IF and ten TACs were generated as described above, and kinetic modeling was performed with these simulated, noise-containing IFs and TACs as described above. Fit parameters were compared to the experimental values, and mean values and standard deviations of the fitted parameters were compared between the bolus and infusion protocols.
Finally, to investigate the influence of sampling frequency on the fit parameters and fitting precision (parameter standard deviations), IF sampling intervals were prolonged from the experimental 1 s to 30 s and 60 s, respectively, by deleting the data between these time points from both the experimental and above simulated noise-containing IFs. Kinetic modeling was performed with the identical simulated noise-containing TACs as used for the complete IF datasets.
Statistical analysis
Data are presented as mean ± SD; error bars in figures represent SD and are further specified in the figure legends and text. Fitted parameters with the simulated IFs and TACs were compared by two-tailed homoscedastic t test. The effects of data smoothing and miscalibration were assessed with paired-sample t test, corrected for multiple comparisons (Bonferroni). Significant differences are indicated with an asterisk (*) for P < 0.05 and double asterisk (**) for P < 0.01.
Results
Fractional blood volume
Fractional blood volume ( v _{ b } , in %) as estimated with the two-tissue compartment model
Full TAC | 50% TAC | Smooth IF | Smooth TAC | Smooth IF and TAC | ||
---|---|---|---|---|---|---|
Cortex | Min. χ^{2 a} | 3.8 ± 4.0 | 4.6 ± 3.4 | 3.7 ± 3.9 | 7.8 ± 6.2 | 6.3 ± 1.9 |
Model fit^{b} | 7.2 ± 4.0 | 9.7 ± 7.2 | 3.7 ± 3.8 | 15.1 ± 7.1 | 6.3 ± 1.8 | |
Hypothalamus | Min. χ^{2} | 12.7 ± 2.7^{c} | Not fitted | Not fitted | Not fitted | 11.1 ± 5.0 |
Model fit | 11.7 ± 1.1^{c} | 11.5 ± 4.1^{c} |
Influence of data smoothing on the fitted rate constants
Figures 2B and 3 show the influence of data smoothing on CMR_{glc} and rate constants. Data smoothing did not affect CMR_{glc} significantly, but significant differences occurred between estimates of all single rate constants with the original TAC and their estimates achieved with any combination of the smoothed data vectors (P < 0.05) with only one exception (comparison K _{1} with smooth IF versus original data, see Figure 3A). In general, data smoothing leads to underestimation of K _{1} and k _{2} by 5% and 4%, respectively, when both TAC and IF were smoothed, and to overestimation by 5% to 15% when only TAC or IF were smoothed.
Delay between IF and TAC, calibration errors
Relative changes in model estimates due to calibration errors
Calibration error scanner/counter | K _{1} | k _{2} | k _{3} | k _{4} | CMR _{glc} | χ ^{2} |
---|---|---|---|---|---|---|
−5% | −7 ± 3%* | −1 ± 6% | +1 ± 5% | +4 ± 8% | −5 ± 2%* | + 9 ± 24% |
+5% | +6 ± 4%* | +1 ± 6% | 0 ± 6% | +4 ± 12% | +6 ± 4%* | +10 ± 28% |
Correction for FDG blood cell uptake
Non-linear regression analysis of experimental IF and simulations of IF and TAC
TACs for the cortex were generated with PMOD from the simulated IFs (before noise was added) and the experimental rate constants. From each generated TAC, ten variations were calculated by the addition of random Gaussian noise as described under the ‘Methods’ section.
FDG kinetic modeling with simulated bolus and experimental and simulated infusion protocols
Discussion
Glucose uptake and metabolism and, therefore, FDG kinetics depend on many physiological factors. Minor deviations in physiological conditions can result in significant differences between the results from FDG PET studies [1, 18, 19]. However, without kinetic modeling and resolution of the single process rate constants of FDG and glucose in the region of interest, it is impossible to conclude whether such differences result from divergences in systemic FDG disposition, inconsistent data analysis or, indeed, differences in glucose transport and phosphorylation in the region of interest. In this work, we applied two-tissue compartment kinetic modeling to exclude the influence of systemic FDG disposition on the results. We focused on the application protocol and parameters that influence data analysis in kinetic modeling once the experimental part is completed. We show that several parameters and conditions which are often not paid much attention for can strikingly affect the modeling results and may lead to erroneous conclusions when comparing experimental results.
We showed that omission of v _{b} in the model equation and even minor flaws in experimental meticulousness can result in substantial distortions of FDG PET kinetic modeling results. Transport parameters were most sensitive to such methodological flaws, but k _{3} and k _{4} were also affected, and even the allegedly robust CMR_{glc} was subject to substantial changes. The sensitivity of the transport parameters to v _{b} and timing errors is a consequence of the shape of the IF: Correct estimation of K _{1} and k _{2} relies on the early time points of the IF and TAC, where equilibration between blood plasma and the free tissue pool occurs.
Our calculations suggest that it is desirable to fix v _{b} for model fitting rather than including it as a fit parameter, even with more than sufficient data points in IF and TAC, as its inclusion in the model did not lead to increased model precision or even an accurate fit of v _{b} itself. The goodness of fit carried little information about v _{b} and the fit estimates obtained for v _{b} are unlikely to reflect the true physiological situation. Even the inclusion of larger vessel structures such as the circle of Willis in the hypothalamic region of interest would not lead to a v _{b} of approximately 12% as suggested by modeling. We, therefore, recommend the use of literature values, e.g., from Chugh et al. [16] for v _{b} in the brain region under investigation. The situation may be different for bolus administration of FDG. At the very start of the scan, when the IF reaches its peak, tissue radioactivity is still low and v _{b} may be better accessible than with our infusion protocol.
Data smoothing did not result in greater precision of parameter estimates but affected estimates of single rate constants significantly. Smoothing the TAC removed at least some information related to v _{b}: The best goodness of fit was shifted away from that of the original data fit along the v _{b} axis. Interpolation without curve smoothing may be the best option, if additional degrees of freedom are required for robust modeling.
Delay between starting times of IF and TAC and timing errors for early blood samples are likely to be among the major causes of variation in previous reports. Without automated sampling tools such as beta probes [20] or coincidence counters operating on a shunt volume [7, 8], it is virtually impossible to get correctly timed samples because of catheter dead volume and the time needed for transfer between animal and measurement device or for blood plasma separation. We, therefore, recommend the substitution of manual sampling with automated, high temporal resolution sampling and to pay particular attention to synchronization of starting time of IF and TAC.
As expected from the impulse response function, systematic errors resulting in the multiplication of the input function by a constant factor, such as calibration errors, can only be compensated by K _{1}. Rate constants k _{2} to k _{4} are in the exponents of the response function, defining the shape of the TAC [3], which is not affected by this kind of error.
The method how the IF is derived from the experimental blood data affects the single rate constants and CMR_{glc}. Based on our results, kinetic modeling with whole blood IF or a constant scaling factor is not recommended. Our comparison of two similar correction functions suggests that minor inter- and intra-individual differences in blood cell uptake of FDG may affect the results of kinetic modeling. This should be taken into account, and individual kinetics of blood cell uptake should be determined when comparing FDG kinetics of a heterogeneous group of animals.
Our well-defined experimental IFs support the notion that infusion instead of bolus injection avoids unpredictable blood activities at the early time points due to non-instant distribution of the FDG in the central, that is, the measurement and input compartment [9]. We conclude from our simulations that loss of information for modeling is negligible at moderate infusion duration of 5 min as compared to bolus administration. Based on our simulation, a 5-min infusion protocol allows for longer intervals between blood samples than a bolus injection. The infusion protocol could thus allow kinetic modeling under conditions where a shunt surgery is not advisable and alternative less invasive blood sampling techniques are required, e.g., in longitudinal studies. We have successfully applied the infusion protocol for FDG kinetic modeling with image-derived IFs [7]. Here, we demonstrate in addition that infusion duration cannot be prolonged further without loss in information for kinetic modeling.
We may have missed a fast initial distribution phase in the simulated IFs of the bolus injection. The simulated IF of bolus V1132 resembled closest the general shape of an FDG bolus IF [15]. Results of this dataset were in agreement with those of the other simulations. For this reason and because an additional peak of short duration would add to the overestimation of K _{1} and possibly other rate constants if sampling intervals are not shortened, we conclude that our interpretation of the simulated data with the 30-s sampling intervals are correct.
There are two other pertinent issues in the quantification of CMR_{glc} which are not addressed in this work. One of them is the LC, which corrects for differences in the kinetics of FDG compared to glucose [5]. The LC can be derived from kinetic modeling results [21], but it does not influence the rate constants of FDG determined in this work (i.e., K _{1} to k _{4} and K _{FDG}). The data in Table 1 all use similar LCs and can, therefore, be directly compared to each other. The second issue is the inclusion of the parameter describing dephosphorylation, k _{4}, in the model [4]. As the results for other parameters were not significantly affected by k _{4} (which was close to zero), we decided to include it in the model for the present study.
Conclusions
To increase the reliability of FDG PET data modeling with the two-tissue compartment model, we recommend FDG infusion over about 5 min; to include an appropriate value for the fractional blood volume in the tissue of interest as well as to correct the IF for blood cell uptake kinetics. Data smoothing was demonstrated to be an inappropriate manipulation, prohibiting precise and accurate modeling. We also show that delays of a few seconds between the start and early sampling of IF and TAC can lead to substantial misestimates. We hope that our findings will contribute toward improved methodological standards in FDG kinetic modeling.
Declarations
Acknowledgments
This work was supported (MFA) by the Swiss National Competence Center for Biomedical Imaging (NCCBI).
Authors’ Affiliations
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