Journal of Cerebral Blood Flow and Metabolism 18:154-160 © 1998 The International Society of Cerebral Blood Flow and Metabolism Published by Lippincott-Raven Publishers, Philadelphia

Calculation of the FDG Lumped Constant by Simultaneous

Measurements of Global Glucose and FDG Metabolism

in Humans

Steen G. Hasselbalch, Peter L. Madsen, Gitte M. Knudsen, *Spren Holm, and Olaf B. Paulson

Departments of Neurology and *Nuclear Medicine, National University Hospital, Rigshospitalet, Copenhagen, Denmark

Summary: The lumped constant defined as the conversion factor between the net uptake of fluoro-2-deoxy-D-glucose (FDG) and glucose was calculated from global CMRglc and from positron emission tomography (PET) using FDG as tracer (CMRpDd. Fifteen healthy, normal volunteers (mean age 24 ±

4 years) were studied. Global CBF and CMRg1c were measured with the Kety-Schmidt technique using 133Xe as tracer, and values were corrected for errors from incomplete diffusion equilibrium for inert gas tracer between brain tissue and cere­bral venous blood. Measurements of CMRpDG were obtained with PET using the dynamic and single-scan methods and the KI-k3 model. Measurements with the Kety-Schmidt technique and PET-FDG were performed simultaneously. Global CBF was 47.1 ± 8.0 mL · 100 g-I . min-t, and CMRglc was 22.8 ±

Determination of the regional glucose metabolism us­

ing positron emission tomography (PET) with I8F_

fluoro-deoxy-D-glucose (FDG) as the tracer is one of the

most widely used PET methods for quantification of re­

gional brain function in humans (Sokoloff et aI., 1977,

Reivich et aI., 1979, Phelps et aI., 1979). Since FDG and

glucose differ with regard to transport across the blood­

brain barrier and phosphorylation through the initial step

in the glycolysis, FDG net uptake (CMRFDG) must be

converted into glucose net uptake or CMRg\c by the

lumped constant (LC) (Sokoloff et aI., 1977).

U sing the Sokoloff three-compartment model, the LC

can be described by the rate constants related to blood-

Received November 26, 1996; final revision received September II, 1997; accepted September 11, 1997.

Supported by grants from the Danish Medical Research Council, the Foundation of 17-12-1981, the Alfred Benzon Foundation, the Lund­beck Foundation, and the Simon F. Hartmann Family Foundation.

Address correspondence and reprint requests to Dr. Steen G. Hasselbalch, Neurobiology Research Unit N9201, National University Hospital, Rigshospitalet, 9, Blegdamsvej, DK-2100 Copenhagen. Den­mark.

Abbreviations used: CMRFDo, 18F-fluoro-deoxY-D-g]ucose net up­take; FDG, 18F-fluoro-deoxY-D-g]ucose; PET, positron emission to­mography; ROI, regions of interest.

154

4.1 fl-mol . 100 g-l . min-I. No difference in CMRpDG was found with the two methods (17.8 ± 1.6 and 18.2 ± 1.3 fl-mol . 100 g-I . min-I, dynamic and single scan methods, respec­tively). Accordingly, the lumped constant ranged from 0.80 ± 0.16 to 0.82 ± 0.15, with a mean value of 0.81 ± 0.15. The mean ratio between phosphorylation of FDG and glucose (k3*lk3) was 0.39 ± 0.25. The discrepancy between the lumped constant determined in this study and previously obtained values can be explained partly by methodologic problems, and we conclude that most of the discrepancy results from previous overestima­tion of global CBF. Key Words: Positron emission tomogra­phy-18F-Fluro-deoxy-D-glucose-Lumped constant-Brain glucose metabolism.

brain barrier transport and phosphorylation of the two

hexoses:

where KI and KI * are unidirectional clearance from

blood to brain of glucose and FDG, respectively, k2 and

k2* are fractional clearance from brain to blood of glu­

cose and FDG, respectively, and k3 and k3 * are fractional

phosphorylation coefficients of glucose and FDG by

hexokinase through the initial step of glycolysis. The LC

can be estimated, provided these parameters are mea­

sured or if a constant relation between them is assumed

(Kuwabara et aI., 1990, Holden et aI., 1991). We have

previously determined the ratio between unidirectional

clearances for FDG and glucose (K 1* IK 1) in humans and

found a mean value of 1.48, irrespective of blood glucose

levels (Hasselbalch et aI., 1996), but the phosphorylation

ratio (k3*lk3) has not been determined in humans, and

several assumptions must be made to calculate the LC

from parameters obtained in a dynamic PET study (Ku­

wabara et aI., 1990). Thus, although this approach is

tempting because it allows for a pixel-by-pixel determi­

nation of the LC, it should be further validated by other

approaches that are less dependent on the chosen model.

CALCULATION OF THE FDG LUMPED CONSTANT 155

The LC can be determined more simply as the con­

version factor between FDG and glucose brain net up­

take. The LC has been calculated as the ratio between net

extraction fractions of FDG and glucose measured dur­

ing steady-state arterial concentrations of the two hexo­

ses in rats (Sokoloff et aI., 1977) and in humans (Reivich

et aI., 1985). Although this approach is simple, it requires

highly accurate determination of the arteriovenous dif­

ferences of FDG and glucose. The LC value of 0.52

determined in man by Reivich and coworkers was, as

pointed out by the authors themselves, underestimated

because of contamination of FDG with labeled mannose.

So far, this is the only time that the LC has been mea­

sured in humans, and the aim of this study was twofold:

1) calculation of the LC by a global method, and 2)

determination of the phosphorylation coefficient from

the CMRFDG and global metabolic rate for glucose

(CMRg1c) values obtained in the current study together

with a previously determined ratio of the transport coef­

ficient. We chose to calculate the LC as the difference

between CMRFDG and the "true" CMRg1c, measured

with the Kety-Schmidt technique and arteriovenous dif­

ferences for glucose «a - V)g1c) (Kety and Schmidt,

1948). Provided reliable values for CMRg1c are obtained

with this technique, the value of the LC depends solely

on the PET-FDG method employed, and we therefore

compared CMRg1c with CMRFDG estimated by different

methods (i.e., dynamic and single-scan methods).

MATERIALS AND METHODS

Fifteen healthy subjects were studied. Infonned consent was obtained after written information. The data presented in this report are derived from two separate studies, each of which were approved by the Central Ethical Committee. Data regard­ing glucose consumption during activation (Madsen et aI., 1995) and data concerning the blood-brain barrier transport of FDG and glucose (Hasselbalch et aI., 1996) have been pub­lished separately. Eight subjects (mean age 24 ± 4 years, five men, three women) were studied with uncovered and closed eyes, ears unplugged, and with moderate noise level. Seven subjects (25 ± 3 years, three men, four women) were studied with eyes covered, in dim light, and a low noise level. All subjects were carefully informed about procedures, and sham blood samples were taken before the measurements to famil­iarize the subjects to the experimental procedures.

Determination of CMRg)c by the Kety-Schmidt technique

Global CBF was measured by the Kety-Schmidt technique (Kety and Schmidt, 1948) in the de saturation 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 aI., 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 aI., 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 PET­FDG 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 aI., 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)g!c' Global meta­bolic rate for glucose was calculated according to Fick's prin­ciple: CMRg\c = CBF x (a - v)g!c'

Determination of CMRFDG We used the PC4096+ PET camera (General Electric Medi­

cal 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 perfonned 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 lO-second intervals from t = 0 to t = 3 minutes, at 20-second intervals from 3 to 5 minutes, at I-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 I-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 cross­calibration factors in the total period of PET -scanning was less than 4%. Global CMRglc 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 perfonned 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 aI., 1985). Rate constants were estimated by a nonlinear least­square fitting procedure of brain and plasma time activity

J Cereb Blood Flow Metab. Vol. 18. No.2, 1998

156 S. G. HASSELBALCH ET AL.

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 CMRpDG was calculated from (C/LC) (Kj* k3*)/(k2* + k3*)' where Cp is plasma glu­cose concentration, LC is the LC set to I, and Kl *, k2 *, and k3 * are the fitted rate constants of the deoxyglucose model (Huang et aI., 1980).

Single-scan method (autoradiographic method). The CMRpDG 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 aI., 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 CMRpDG were calculated assuming a 60:40 ratio between gray and white matter.

Calculation of the phosphorylation coefficient The phosphorylation coefficient was determined from

where K, *, k2 *, and k3 * are the fitted rate constants of the deoxyglucose model, and K* is the net clearance of FDG equal to (K

1 * k3 *)/(k2 * + k3 *) (Kuwabara et aI., 1990), and

(3)

which combined yields

k3*/k3 = (CMRpDG/CMRg]c - (Kj*/K]) . K*/Kj*)/(l - K*/K]*) (4)

Values for CMRpDG, K*, and Kl * were determined from the different PET-FDG methods described earlier, and (K

1 */Kj)

was set to 1.48 (Hasselbalch et aI., 1996).

Blood sample analysis Blood samples for determination of plasma glucose concen­

trations 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 ILL 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),

J Cereb Blood Flow Me/ab, Vol. 18, No.2, 1998

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)g1c was calculated from glucose concentrations in arterial and venous plasma corrected to corresponding whole blood values, as described previously (Madsen et aI., 1995).

RESULTS

In the 15 subjects studied, plasma glucose was 5.26 ±

0.61 mmollL (mean ± SD). Global CBF was 47.1 ± 8.0

mL· 100 g-l . min-I, (a - V)g1c was 0.49 ± 0.06 mmol/L,

and the resulting global CMRglc was 22.8 ± 4.1

J..Lmol . 100 g-l . min-I.

The FDG rate constants obtained with PET from

whole-slice ROI are listed in Table 1 together with the

resulting global net clearance (K*) and CMRpDG• The

CMRpDG calculated from gray and white matter differed

significantly from CMRpDG calculated from whole-slice

ROI (16.5 ± 1.4 versus 17.8 ± 1.6, P < 0.0001).

The LC calculated as the ratio between CMRpDG and

CMRg1c ranged from 0.81 to 0.82, depending on the ap­

plied PET method (Table 2). Since there was no signifi­

cant difference between the two PET methods used,

mean values also are listed. The mean phosphorylation

ratio calculated from equation 4 was 0.39 ± 0.25 (Table

2). It was thus possible to calculate LC from equation 2

using constant values for K 1 * IK I (1.48, Hasselbalch et

aI., 1996) and k3*lk3 (0.39, the current study), and obtain

an average value for CMRglc almost identical to that

obtained from Fick's principle (22.8 ± 4.1 versus 22.4 ±

1.5) (Table 2). The CMRg1c calculated by this method

differs substantially from CMRg1c calculated by using a

fixed LC value of 0.52 (Reivich et aI., 1985) (22.4 ± 1.5

versus 35.0 ± 2.5, P < 0.00001) .

DISCUSSION

Methodologic considerations Determination of the LC from measurements of CMR­

g1c performed simultaneously with the Kety-Schmidt

technique and the PET-FDG technique is a straightfor­

ward procedure. The two methods do, however, differ

with respect to the following: (1) the period of measure­

ment, and (2) brain regions included in the global aver­

age measure for CMRg1c 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 tech­

nique. However, the entire study was performed during

CALCULATION OF THE FDG LUMPED CONSTANT

TABLE 1. Rate constants and CMRFDG determined from dynamic PET-FDG in 15 healthy subjects in a resting condition

Global whole slice Grey matter White matter 60:40

K,* (mL . g-I . min-I) 0.091 ± 0.011 0.104 ± 0.013 0.048 ± 0.006 0.081 ± 0.009t k*2* (g-

l . min-I) 0.118 ± 0.027 0.118 ± 0.035 0.082 ± 0.016 0.104 ± 0.025t k3* (g-I . min-I) 0.071 ± 0.014 0.080 ± 0.017 0.040 ± 0.009 0.064 ± 0.012t Vp (%) 5.4 ± 1.3 K* (mL . g-

l . min-I) 0.034 ± 0.005 0.042 ± 0.006 0.016 ± 0.003 0.031 ± 0.004t CMRpDG, dynamic

(fLmol . 100g-' . min-I) 17.8 ± 1.6 16.5 ± l.4t CMRpDG, single scan

(fLmol . 100g-' . min-I) 18.2 ± 1.3

CMRpDG, 18F-fluro-deoxy-D-glucose net uptake; PET-FDG, positron emission tomography with FDG as a tracer. Values are mean ± SD. K, *: unidirectional clearance from blood to brain; k2 *: fractional clearance from brain to blood; k3 *: fractional phosphorylation rate of FDG to FDG-6-P; Vp: plasma volume in brain; K*: net clearance of FDG from blood to brain equal to (K

I* k3*)/(k2* + k3*)' CMRFDG, dynamic: (plasma glucose· K*)ILC, where LC:1. CMRpDG,

single scan: CMRpDG calculated from the autoradiographic equation as described in methods. Global whole slice: global rate constants calculated from whole slices as described in methods. Grey matter, White matter: rate constants determined from grey matter and white matter respec­tively. 60:40, rate constants calculated by assuming a 60:40 ratio between grey and white matter.

t p < 0.0001, paired I-test compared to global whole slice.

157

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 ter­

mination of the Kety-Schmidt measurement, that they

would not have caused any significant change in the

calculated CMRFDG. Methodologic considerations re­

garding brain areas included in the global average values

obtained with the Kety-Schmidt technique have been dis­

cussed in detail previously, and here it suffices to con­

clude 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 aI., 1948; Lassen, 1959;

Madsen et aI., 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 133

Xe 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

TABLE 2. Global metabolic rate of FDG and lumped constant in 15 healthy subjects in a resting condition

Dynamic scanning Single scan

(autoradiographic) Mean Fixed LC Fixed ratios

(K,*/K, = 1.48; k*/k3 = 0.39)

CMRpD(; (fLmol . 100g-' . min-I)

17.8 ± 1.6

18.2 ± 1.3 18.0 ± 1.4

LC

0.80 ± 0.16

0.82 ± 0.15 0.81 ± 0.15

0.52

0.81 ± 0.07

0.38 ± 0.27

0.41 ± 0.25 0.39 ± 0.25

CMRglc (fLmol . 100g-1 . min-I)

35.0 ± 2.5t

22.4 ± 1.5

CMRpDG, '8F-fluro-deoxy-D-glucose net uptake; CMRg1c' global metabolic rate for glucose. Values are mean ± SD. CMRpDG: Cerebral metabolic rate for FDG calculated from PET-FDG with lumped constant = 1. LC: lumped constant calculated as the ratio between individual CMRpDG and CMRg1c values. Dynamic scanning: CMRpDG calculated from rate constants estimated from whole slice ROI (see Methods). Single scan (autoradiographic) = CMRFDG calculated from last scan of dynamic sequence using the autoradiographic method and whole slice ROL k*ik3: phosphorylation ratio between FDG and glucose calculated from equation (4). No significant differences were found between the two methods and therefore pooled mean values of dynamic and single scan methods are also shown. Fixed LC: CMRglc calculated from CMRpDG (single scan method) using a fixed LC value of 0.52 (Reivich et aI., 1985). Fixed ratios: LC and CMRglc calculated from single scan CMRpDG using fixed ratios in equation (2); Kl*/K

I = 1.48 (Hasselbalch et aI., 1996); k*ik3 = 0.39 (mean value determined in' present study).

t p < 0.0001 compared to CMRglc calculated in the present study (22.4 ± 1.5).

J Cereb Blood Flow Metab, Vol. 18, No.2, 1998

158 S. G. HASSELBALCH ET AL.

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 underes­

timation of CBF of 2%, 5%, and 10%, respectively, in

both the high and low CBF example. It is unlikely that

this contamination of 133

Xe 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 133

Xe sample, in­

creasing the flushing volume to five to six times the dead

space volume. We conclude that this possible error ex­

plains only a small part of the discrepancy between our

CBF values and those previously reported (Scheinberg

and Stead, 1949; Novack et aI., 1953; Gottstein et aI.,

1963; Cohen et aI., 1967; Takeshita et aI., 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

PDG was the same outside as inside the field of view, the

measured value is representative of the global value.

Almost identical values for CMRpDG were obtained

with the whole-slice approach, regardless of the method

used (dynamic or single scan). When global rate con­

stants were determined from gray and white matter, a

significant underestimation of CMRpDG 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 aI., 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 si­

multaneous measurements of CMRpDG and CMRgIc

was higher than the previously calculated values of 0.42

to 0.60 (Phelps et aI., 1979, Reivich et aI., 1985, Brooks

et aI., 1987; Kuwabara et aI., 1990). Differences in glob­

al FDG net clearance (K*) or CMRpDG only partly ex­

plain this difference. Brooks and coworkers obtained a

CMRpDG value of 15.0 f1mol . 100 g-l . min-

I compared

with 18.1 f1mol . 100 g-l . 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 CMRpDG• How­

ever, the higher LC value may derive from the use of

different global average values for CMRglc applied in the

J Cereb Blood Flow Metab. Vol. 18. No.2. 1998

calculation of the LC: the CMRglc value of 23 f1mol . 100

g-l . min-1

used in the current study is considerably

lower than the value of 30 f1mol . 100 g-l . min-I

, which

has been used a standard global value for CMRglc, either

for direct calculation of LC (Phelps et aI., 1979; Brooks

et aI., 1987; Kuwabara et aI., 1990) or for validation of

obtained values for LC (Reivich et aI., 1985). The global

CMRg1c value of 30 f1mol . 100 g-l . 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; No­

vack et aI., 1953; Gottstein et aI., 1963; Cohen et aI.,

1967; Takeshita et aI., 1974). However, despite the solid

theoretical foundation of the Kety-Schmidt technique,

the mean global CBF value of 53 mL . 100 g-l . min-1

derived from these studies probably represents an over­

estimation of the true global CBF value (Lassen, 1959;

Madsen et aI., 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 aI., 1967), and as a conse­

quence, the global values for CBF and CMRglc 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 a!., 1953;

Gottstein et a!., 1963; Cohen et aI., 1967; Takeshita et aI.,

1974). Several approaches to correct for this systematic

overestimation have been developed (Lassen and Lane,

1961; Madsen et aI., 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-l . min-

1 and 25 f1mol . 100 g-

l .

min -I

, respectively (Lassen and Lane, 1961; Cohen et

aI., 1967; Madsen et aI., 1993). The CMRglc value that

was obtained in the current study was close to the CMR­

g1c values obtained in these studies. It is also similar to

the CMRg1c value obtained with ll

C-labeled glucose by

Blomqvist and others (1990). In conclusion, in calcula­

tions of the LC (Phelps et aI., 1979; Brooks et aI., 1987;

Kuwabara et aI., 1990), the applied value for CMRg1c has

probably been higher than the true CMRg1c 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 calcu­

lated LC values of 0.42 to 0.60 (Phelps et aI., 1979;

Brooks et aI., 1987; Kuwabara et aI., 1990).

In only one study, direct measurement of the LC has

been attempted (Reivich et aI., 1985). Reivich and col­

leagues calculated the LC as the ratio between net ex­

traction 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

CALCULATION OF THE FDG LUMPED CONSTANT 159

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 im­

purity 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 cal­

culation 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 de­

terminations 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 differ­

ences for glucose are mean values obtained from six to

eight samples, which tends to increase the accuracy.

Other methodologic problems may explain the discrep­

ancy, and further studies are needed to clarify this issue.

However, both studies (Reivich et aI., 1985; the current

study) indicate that the LC is higher than 0.52. This is

consistent with the observation by Frackowiak and oth­

ers (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 ar­

rived 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 glu­

cose. Although pentobarbital anesthesia affects the ab­

solute values for transport and phosphorylation of FDG

and glucose, it is unlikely that the transport and phos­

phorylation ratios are affected. The transport coefficient

obtained by Crane and colleagues (FGD/glucose = 1.67

± 0.07) was similar to that obtained in non sedated

healthy volunteers (1.48 ± 0.22, Hasselbalch et aI.,

1996), which speaks against a significant effect of pen­

tobarbital on the transport ratio. The observed and pre­

dicted FDG LC values in the study of Crane and cowork­

ers (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 deter­

mined 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 pre-

vious overestimation of global CBF, and subsequently,

global CMRg!c.

Kuwabara and associates (1990) and Holden and oth­

ers (1991) have proposed that the LC can be determined

regionally from dynamic PET data, assuming that the

FDG/glucose blood-brain barrier transport ratio (KJ */

KJ) as well as the phosphorylation ratio (k3 *lk3) are

known and constant. In our study, we found a mean

k3*lk3 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

aI., 1983). Equation 2, with fixed ratios of 1.48 (Hassel­

balch et aI., 1996) and 0.39 for KJ*/KJ and k3*lk3' re­

spectively, may generate reliable CMRglc values from

PET-FDG as shown in the current study, but the exact

value of the phosphorylation coefficient should be cor­

roborated 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 aI., 1989).

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

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