Calculation of the FDG Lumped Constant by Simultaneous Measurements of Global Glucose and FDG Metabolism in Humans

Determination of CMRglc by the Kety-Schmidt technique

Global CBF was measured by the Kety-Schmidt technique (Kety and Schmidt, 1948) in the desaturation mode, using ¹³³Xe as the flow tracer. Cerebral venous blood was sampled from a catheter inserted percutaneously low on the neck into the internal jugular vein. The catheter tip was advanced to the base of the skull, and the correct placement was verified as described elsewhere (Hasselbalch et al., 1994). Arterial blood was sampled from a catheter in the radial artery. Both catheters had the same dead space volume (0.75 mL). Measurements of global CBF were performed as previously described in detail (Madsen et al., 1993). In brief, the brain was saturated by an intravenous infusion of ¹³³Xe dissolved in saline at a constant rate of approximately 15 MBq · min⁻¹ for 30 minutes. A 1.5-mL dead space volume was drawn simultaneously from both catheters, immediately before 1 mL of blood was drawn into preweighed syringes. Blood samples were obtained at exact times, t = −2, −1, 0, 0.5, 1, 2, 3, 4, 6, 8, and 10 minutes, where t = 0 denotes the time when the Xe infusion was terminated and the CBF study was started. Also at time t = 0, the PET-FDG study was started, and the global CBF was thus measured during the first 10 minutes of the PET-FDG study. To avoid loss of ¹³³Xe gas by diffusion, the syringes were reweighed immediately after each run and placed in sealed vials for counting in a well counter (COBRA 5003, Packard Instrument, Downers Grove, IL, U.S.A.). The measured CBF values were corrected for systematic overestimation of flow values caused by incomplete tracer washout at the end of the measuring period (Madsen et al., 1993). From time t = 0 to t = 25 minutes, six to eight paired samples of arterial and jugular venous blood were obtained for determinations of (a – v)_glc. Global metabolic rate for glucose was calculated according to Fick's principle: CMR_glc = CBF × (a – v)_glc.

Determination of CMRFDG

We used the PC4096+ PET camera (General Electric Medical Systems, Milwaukee, WI, U.S.A.), yielding 15 consecutive slices with a slice thickness of 6.7 mm and a spatial resolution in the image plane of 6.7 mm. Slices were placed parallel to the canthomeatal line (which is a line through the lateral canthus of the eye and the external meatus of the ear) with midslice planes from approximately 10 to 103 mm above the canthomeatal line. With this position, only the brain stem and the small top convexity of the brain are not in the field of view. After placement of the subject in the scanner, a transmission scan used for attenuation correction was performed immediately before the activity scan. At time t = 0, 185 to 210 MBq FDG in 10 mL of saline was injected as a bolus over 20 seconds through an antecubital catheter followed by 5 to 10 mL of saline at the same infusion rate. One-milliliter blood samples were drawn simultaneously from the jugular vein and the radial artery at 10-second intervals from t = 0 to t = 3 minutes, at 20-second intervals from 3 to 5 minutes, at 1-minute intervals from 5 to 10 minutes, at 2-minute intervals from 10 to 20 minutes, and at 5-minute intervals for the rest of the scanning period. Dynamic scanning was started at t = 0 with the following scan sequence: 10 6-second scans (0 to 1 minutes), 3 20-second scans (1 to 2 minutes), 8 1-minute scans (2 to 10 minutes), 5 2-minute scans (10 to 20 minutes), 5 5-minute scans (20 to 45 minutes) in eight subjects, and 8 5-minute scans (20 to 60 minutes) in seven subjects. Cross-calibration between scanner and gamma counter was performed every week, and mean values for the period were used. The coefficient of variation of cross-calibration factors in the total period of PET-scanning was less than 4%. Global CMR_glc was calculated from PET by two different methods: 1) dynamic method, and 2) single-scan method (autoradiographic method).

Dynamic method. Rate constants were calculated from 15 regions of interest (ROI), with each ROI containing a whole slice, and mean global values were obtained by weighting the 15 ROI with their area: Whole-slice ROI were defined by the 25% of maximal image activity threshold, and ROI were hand drawn accordingly. Correction for CSF space was performed by subtracting 2.5% from this area. This value was chosen because the total CSF volume (subarachnoid space plus ventricles) constitutes 2.5% of the total intracranial volume in a comparable section of the brain in young adults (Schwartz et al., 1985). Rate constants were estimated by a nonlinear least-square fitting procedure of brain and plasma time activity curves. k₄* (dephosphorylation of FDG-6-phosphate) was considered negligible during the scanning period and therefore not included in the model. Tracer activity in brain vasculature was subtracted after plasma volume in the brain had been fitted as an additional parameter. The value for CMR_FDG was calculated from (C_p/LC) (K₁* k₃*)/(k₂* + k₃*), where C_p is plasma glucose concentration, LC is the LC set to 1, and K₁*, k₂*, and k₃* are the fitted rate constants of the deoxyglucose model (Huang et al., 1980).

Single-scan method (autoradiographic method). The CMR_FDG was calculated by the single-scan method, as described by Sokoloff et al. (1977) and by Reivich et al. (1979). The last 5-minute scan in the dynamic sequence was used for calculation, that is, in eight subjects the final scans were obtained from 40 to 45 minutes after injection, and in seven subjects from 55 to 60 minutes. Whole-slice ROI (defined as described for the dynamic method) were used. The correction for nonmetabolized FDG in brain and for lag in equilibration of the tissue precursor pool behind the plasma (Sokoloff et al., 1977) were calculated using the rate constants obtained from the same whole-slice ROI as described earlier. Activity in the last scan used for the single-scan method was corrected for remaining tracer activity in the brain vasculature, assuming a mean cerebral blood volume of 3%.

Finally, we compared the dynamic whole-slice approach to a determination of rate constants in gray and white matter (six regions each at midlevel of brain). Mean gray and white matter rate constants were determined from weighted averages in these ROI as described earlier, and, subsequently, global rate constants and global CMR_FDG were calculated assuming a 60:40 ratio between gray and white matter.

Calculation of the phosphorylation coefficient

The phosphorylation coefficient was determined from

L C = ( k 3 ∗ / k 3 ) + ( ( K 1 ∗ / K 1 ) - ( k 3 ∗ / k 3 ) ) ( K ∗ / K 1 ∗ )

(2)

where K₁*, k₂*, and k₃* are the fitted rate constants of the deoxyglucose model, and K* is the net clearance of FDG equal to (K₁* k₃*)/(k₂* + k₃*) (Kuwabara et al., 1990), and

L C = C M R F D G / C M R g l c

(3)

which combined yields

k 3 ∗ / k 3 = ( C M R F D G / C M R g l c - ( K 1 ∗ / K 1 ) ⋅ K ∗ / K 1 ∗ / ( 1 - K ∗ / K 1 ∗ )

(4)

Values for CMR_FDG, K*, and K₁* were determined from the different PET-FDG methods described earlier, and (K₁*/K₁) was set to 1.48 (Hasselbalch et al., 1996).

Blood sample analysis

Blood samples for determination of plasma glucose concentrations were drawn into vials containing fluoride–ethylenediamine tetraacetic acid, stored on ice for 5 minutes, centrifuged, and analyzed in duplicate within 15 minutes on a Beckman Glucose Analyzer (Beckman Instruments, Fullerton, CA, U.S.A.). The FDG blood samples were immediately placed on ice and centrifuged, and 500 μL of plasma was taken for gamma counting (COBRA 5003, Packard Instrument, Downers Grove, IL, U.S.A.). The blood samples used in the PET-FDG and CBF measurements contained gamma activity from both ¹³³Xe (decay T2 = 5.25 days) and ¹⁸F-FDG (decay T2 = 110 minutes). Energy windows were set around the energy peak of each tracer (¹³³Xe = 70 to 90 keV, ¹⁸F = 461 to 561 keV), and spillover correction was applied. By extending the time interval from blood sampling to gamma counting of the blood samples, downspill from the ¹⁸F window to the ¹³³Xe window decreased rapidly. The blood samples were counted continuously for the following 12 hours, and the optimal counting time was found to be 8 to 10 hours after injection, where the crosstalk correction from FDG into the ¹³³Xe-window was small and no detectable diffusion of ¹³³Xe from the vials had occurred. Cerebral (a – v)_glc was calculated from glucose concentrations in arterial and venous plasma corrected to corresponding whole blood values, as described previously (Madsen et al., 1995).

Methodologic considerations

Determination of the LC from measurements of CMR_glc performed simultaneously with the Kety-Schmidt technique and the PET-FDG technique is a straightforward procedure. The two methods do, however, differ with respect to the following: (1) the period of measurement, and (2) brain regions included in the global average measure for CMR_glc are not necessarily completely identical with the two methodologies.

The Kety-Schmidt technique measures CBF over a time period of 10 minutes, whereas it takes 45 to 60 minutes to complete a study with the PET-FDG technique. However, the entire study was performed during conditions in which external stimuli were minimized. The entrapment of FDG in the brain is a function of the plasma activity that decreases with time, which diminish the effective time window of the PET-FDG scanning. It is therefore reasonable to assume that no significant changes in the rate of cerebral FDG uptake occurred during the PET study, or if changes occurred after termination of the Kety-Schmidt measurement, that they would not have caused any significant change in the calculated CMR_FDG. Methodologic considerations regarding brain areas included in the global average values obtained with the Kety-Schmidt technique have been discussed in detail previously, and here it suffices to conclude that extracerebral contamination of internal jugular blood is small and that unilateral cerebral blood flow measured from one internal jugular vein represent global cerebral blood flow (Shenkin et al., 1948; Lassen, 1959; Madsen et al., 1993). However, one point needs further comments. In our setup with numerous blood samples, dead space in both the arterial and venous catheters was minimized (0.75 mL) to keep the total sampled blood volume as low as possible. Before each sample, 1.5 mL blood was drawn, but this volume may not have been be sufficient to completely flush the catheter from residual blood containing a higher concentration of ¹³³Xe during the clearance of the tracer. This potential error affects both arterial and venous samples, thus diminishing the resulting error in estimation of CBF. The effect on CBF was calculated from two Kety-Schmidt experiments, one with high and one with low flow (59.5 and 37.1 mL, respectively). A contamination of 10%, 25%, and 50% blood from the previous sample resulted in an underestimation of CBF of 2%, 5%, and 10%, respectively, in both the high and low CBF example. It is unlikely that this contamination of ¹³³Xe from the previous sample should lead to an underestimation of CBF by more than a small percentage because several blood samples for arteriovenous differences for FDG, glucose, lactate, and oxygen were obtained between each ¹³³Xe sample, increasing the flushing volume to five to six times the dead space volume. We conclude that this possible error explains only a small part of the discrepancy between our CBF values and those previously reported (Scheinberg and Stead, 1949; Novack et al., 1953; Gottstein et al., 1963; Cohen et al., 1967; Takeshita et al., 1974).

The PET scanner used in the current study had an axial field of view of 10 cm, and only a small part of the brain was outside the field of view. Assuming that mean CMR_FDG was the same outside as inside the field of view, the measured value is representative of the global value.

Almost identical values for CMR_FDG were obtained with the whole-slice approach, regardless of the method used (dynamic or single scan). When global rate constants were determined from gray and white matter, a significant underestimation of CMR_FDG was found (Table 1). This underestimation is most likely caused by inclusion of white matter in the gray matter ROI because of the limited spatial resolution of the PET-scanner. The single-scan method is not affected to the same degree by errors in rate constants (Sokoloff et al., 1977). Therefore the single-scan method may be more robust (coefficient of variation 7% compared with 9% for the dynamic methods), and for further analysis, we only looked at the single-scan method and the dynamic whole-slice method, which yielded almost identical results.

Absolute values for CMRFDG and CMRglc

The LC value obtained in the current study from simultaneous measurements of CMR_FDG and CMR_glc was higher than the previously calculated values of 0.42 to 0.60 (Phelps et al., 1979, Reivich et al., 1985, Brooks et al., 1987; Kuwabara et al., 1990). Differences in global FDG net clearance (K*) or CMR_FDG only partly explain this difference. Brooks and coworkers obtained a CMR_FDG value of 15.0 μmol · 100 g⁻¹ · min⁻¹ compared with 18.1 μmol · 100 g⁻¹ · min⁻¹ in the current study, whereas Reivich and coworkers obtained a global K* close to ours (0.30, calculated from mean gray and white matter rate constants assuming a 60:40 ratio between gray and white matter). Therefore, we cannot explain the large LC discrepancy by differences in CMR_FDG. However, the higher LC value may derive from the use of different global average values for CMR_glc applied in the calculation of the LC: the CMR_glc value of 23 μmol · 100 g⁻¹ · min⁻¹ used in the current study is considerably lower than the value of 30 μmol · 100 g⁻¹ · min⁻¹, which has been used a standard global value for CMR_glc, either for direct calculation of LC (Phelps et al., 1979; Brooks et al., 1987; Kuwabara et al., 1990) or for validation of obtained values for LC (Reivich et al., 1985). The global CMR_glc value of 30 μmol · 100 g⁻¹ · min⁻¹ derived from previous studies using Fick's principle where global CBF was measured with the Kety-Schmidt technique, and subsequently multiplied with cerebral arteriovenous differences for glucose (Scheinberg and Stead, 1949; Novack et al., 1953; Gottstein et al., 1963; Cohen et al., 1967; Takeshita et al., 1974). However, despite the solid theoretical foundation of the Kety-Schmidt technique, the mean global CBF value of 53 mL · 100 g⁻¹ · min⁻¹ derived from these studies probably represents an overestimation of the true global CBF value (Lassen, 1959; Madsen et al., 1993). In the application of the Kety-Schmidt technique, diffusion equilibrium for inert gas tracer between the brain and cerebral venous blood is not reached. Only one of the five studies corrected for this nonequilibrium (Cohen et al., 1967), and as a consequence, the global values for CBF and CMR_glc in the remaining four studies lead to an overestimation of the mean global value derived from these five studies (Scheinberg and Stead, 1949; Novack et al., 1953; Gottstein et al., 1963; Cohen et al., 1967; Takeshita et al., 1974). Several approaches to correct for this systematic overestimation have been developed (Lassen and Lane, 1961; Madsen et al., 1993). When values obtained with the Kety-Schmidt technique are corrected for errors caused by incomplete tracer equilibrium, CBF and CMR_glc are 45 mL · 100 g⁻¹ · min⁻¹ and 25 μmol · 100 g⁻¹ · min⁻¹, respectively (Lassen and Lane, 1961; Cohen et al., 1967; Madsen et al., 1993). The CMR_glc value that was obtained in the current study was close to the CMR_glc values obtained in these studies. It is also similar to the CMR_glc value obtained with ¹¹C-labeled glucose by Blomqvist and others (1990). In conclusion, in calculations of the LC (Phelps et al., 1979; Brooks et al., 1987; Kuwabara et al., 1990), the applied value for CMR_glc has probably been higher than the true CMR_glc value, and consequently, the LC value would be underestimated, and this may account for most of the difference between the LC value in the current study and previously calculated LC values of 0.42 to 0.60 (Phelps et al., 1979; Brooks et al., 1987; Kuwabara et al., 1990).

In only one study, direct measurement of the LC has been attempted (Reivich et al., 1985). Reivich and colleagues calculated the LC as the ratio between net extraction fractions of FDG and glucose measured during steady-state arterial concentrations of the two hexoses. The LC value of 0.52 from this study is considerably lower than the current value. Part of this difference can be explained by a 15% to 20% impurity in the FDG used by Reivich and coworkers. This was calculated by the authors to represent a 12% to 16% underestimation of their LC, and, corrected for this impurity, the LC value should be 0.59 to 0.62. The purity of the FDG used in the current study was in the range of 95% to 99%, but impurity of FDG cannot account for the entire difference between the study of Reivich and colleagues (1985) and the current study. The most critical assumption of the method used by Reivich and coworkers states that no significant dephosphorylation of FDG occurs during the experiment (k₄* = 0), but the effect of k₄* on the calculation of LC by this method has not been validated. If dephosphorylation occurs, the net extraction fraction of FDG continues to decrease with time, and the method will underestimate LC. Both studies rely on accurate determinations of arteriovenous differences of glucose (and FDG in the study by Reivich and coworkers), but in the latter study, the extraction fractions for glucose and FDG with time are plotted and used for fitting an asymptotic value equal to LC. Variation in these extraction fractions therefore significantly affects the LC calculation, whereas in the current study, the arteriovenous differences for glucose are mean values obtained from six to eight samples, which tends to increase the accuracy. Other methodologic problems may explain the discrepancy, and further studies are needed to clarify this issue. However, both studies (Reivich et al., 1985; the current study) indicate that the LC is higher than 0.52. This is consistent with the observation by Frackowiak and others (1988), who calculated the LC from cerebral oxygen metabolism by assuming a molar ratio between oxygen and glucose metabolism of 5.6 (Lassen, 1959), and arrived at a LC value of 0.75. Crane and coworkers (1983) measured the FDG LC by the brain uptake index method in the pentobarbital-anesthetized rat and compared the observed value with a value predicted from measured kinetics of transport and metabolism of FDG and glucose. Although pentobarbital anesthesia affects the absolute values for transport and phosphorylation of FDG and glucose, it is unlikely that the transport and phosphorylation ratios are affected. The transport coefficient obtained by Crane and colleagues (FGD/glucose = 1.67 ± 0.07) was similar to that obtained in nonsedated healthy volunteers (1.48 ± 0.22, Hasselbalch et al., 1996), which speaks against a significant effect of pentobarbital on the transport ratio. The observed and predicted FDG LC values in the study of Crane and coworkers (1983) were 0.77 and 0.85, and thus in the same order of magnitude as the value obtained in the current study. In conclusion, the discrepancy between the LC determined in this study and previously obtained values can be partly explained by methodologic problems, and it is concluded that most of the discrepancy results from previous overestimation of global CBF, and subsequently, global CMR_glc.

Kuwabara and associates (1990) and Holden and others (1991) have proposed that the LC can be determined regionally from dynamic PET data, assuming that the FDG/glucose blood–brain barrier transport ratio (K₁*/K₁) as well as the phosphorylation ratio (k₃*/k₃) are known and constant. In our study, we found a mean k₃*/k₃ ratio of 0.39. Although the SD was relatively large, the value is in the same order of magnitude as the previously reported value in rat brain of 0.55 (Crane et al., 1983). Equation 2, with fixed ratios of 1.48 (Hasselbalch et al., 1996) and 0.39 for K₁*/K₁ and k₃*/k₃, respectively, may generate reliable CMR_glc values from PET-FDG as shown in the current study, but the exact value of the phosphorylation coefficient should be corroborated by future experiments, thus further validating the kinetic approach. Also notice that the method applies only to normal brain tissue because the phosphorylation coefficient has been shown to vary considerably between normal and pathologic brain tissue (Kapoor et al., 1989).

Acknowledgment: We gratefully acknowledge the expert technical assistance of Karin Stahr and Gerda Thomsen.