Direct measurement of the lumped constant for 2-deoxy-[1-14C]glucose in vivo in human skeletal muscle

Tapio Utriainen1, Stefania Lovisatti2, Sari Mäkimattila1, Alessandra Bertoldo2, Susan Weintraub3, Ralph DeFronzo3, Claudio Cobelli2, and Hannele Yki-Järvinen1

1 Division of Diabetology, Department of Medicine, University of Helsinki, FIN-00029 HUCH, Helsinki, Finland; 2 Department of Electronics and Informatics, University of Padova, 35131 Padua, Italy; and 3 The University of Texas Health Science Center at San Antonio, San Antonio, Texas 78229


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INTRODUCTION
SUBJECTS AND METHODS
RESULTS
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The lumped constant (LC) is used to convert the clearance rate of 2-deoxy-D-glucose (2-DGCR) to that of glucose (GlcCR). There are currently no data to validate the widely used assumption of an LC of 1.0 for human skeletal muscle. We determined the LC for 2-deoxy-[1-14C]glucose (2-DG) in 18 normal male subjects (age, 29 ± 2 yr; body mass index, 24.8 ± 0.8 kg/m2) after an overnight fast and during physiological (1 mU · kg-1 · min-1 insulin infusion for 180 min) and supraphysiological (5 mU · kg-1 · min-1 insulin infusion for 180 min) hyperinsulinemic conditions. Normoglycemia was maintained with the euglycemic clamp technique. The LC was measured directly with the use of a novel triple tracer-based method. [3-3H]glucose, 2-[1-14C]DG, and [12C]mannitol (Man) were injected as a bolus into the brachial artery. The concentrations of [3-3H]glucose and 2-[1-14C]DG (dpm/ml plasma) and of Man (µmol/l) were determined in 50 blood samples withdrawn from the ipsilateral deep forearm vein over 15 min after the bolus injection. The LC was calculated by a formula involving blood flow calculated from Man and the GlcCR and 2-DGCR. The LC averaged 1.26 ± 0.08 (range 1.06-1.43), 1.15 ± 0.05 (0.99-1.39), and 1.18 ± 0.05 (0.97-1.37) under fasting conditions and during the 1 and 5 mU · kg-1 · min-1 insulin infusions (not significant between the different insulin concentrations, mean LC = 1.2, P < 0.01 vs. 1.0). We conclude that, in normal subjects, the LC for 2-DG in human skeletal muscle is constant over a wide range of insulin concentrations and averages 1.2.

glucose uptake; insulin; positron emission tomography; isotope; modeling


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ABSTRACT
INTRODUCTION
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SOKOLOFF ET AL. (41) first applied 2-deoxy-[1-14C]glucose (2-DG or 2-[1-14C]DG) and an autoradiographic method to measure local cerebral glucose utilization in the rat. Subsequently, [2-18F]fluoro-2-deoxy-D-glucose ([18F]FDG) has been used for the visualization and quantitation of regional glucose uptake with positron emission tomography (PET) in several human tissues such as brain (36), myocardium (15), and skeletal muscle (33). However, 2-DG is an analog, not an ideal tracer, and thus, if glucose transporters or hexokinases differentiate between 2-DG and glucose, the fractional uptake rate of the tracer (2-DG) may not equal the fractional uptake rate of the tracee (glucose). A correction factor has therefore been used to correct for any differences in the transport and phosphorylation between 2-DG and glucose when converting the clearance rates of 2-DG (2-DGCR) to those of glucose (GlcCR). This term is called the lumped constant (LC) (37, 41). More specifically, the LC for 2-DG is used to convert 2-DGCR to GlcCR.

2-DG is transported into the muscle cell by the same carriers as glucose (7, 19). Glucose transporters seem to have approximately the same affinity for 2-DG as for glucose (7, 23), whereas the affinity of hexokinase for glucose in skeletal muscle is 4- to 10-fold higher than that for 2-DG (7, 16, 19). Thus the LC is dependent on the relative rates of 2-DG and glucose transport and phosphorylation and the contribution of these reactions to the overall rate of glucose uptake in the muscle tissue. The LC might also be dependent on specific study conditions such as insulin and competing substrate concentrations or oxygen availability, as recently suggested by studies performed using the isolated perfused working rat heart preparation (12, 18). By measuring 2-deoxy-[1-3H]glucose (2-[1-3H]DG) (14) or 2-[1-14C]DG (4, 25) and glucose uptake in rat skeletal muscle, Ferré et al. (14) found the LC to range from 0.76 to 0.91 basally [0.78-1.05 in (4)] and from 0.95 to 1.20 during insulin stimulation [not significant (NS) for basal vs. insulin] in isolated soleus, extensor digitorum longus, and epitrochlearis muscles, whereas Mészáros et al. (25) found a basal LC of 0.49 and an LC of 0.59 during insulin stimulation in epitrochlearis muscle (NS for basal vs. insulin). When muscle glucose uptake was measured in normal subjects with the forearm catheterization technique (46) and with the [18F]FDG-positron emission tomography technique ([18F]FDG-PET, assuming an LC of 1.0), comparable rates of glucose uptake were found (33). In the latter study, the measurements of glucose uptake were, however, performed in different groups of subjects with the two techniques. There are at present no studies in which the LC for 2-DG (or for [18F]FDG) have been measured directly in intact human skeletal muscle in vivo.

In the present study, we determined the LC for 2-DG across forearm tissues in normal subjects. Serum insulin concentrations were chosen to represent postabsorptive, postprandial, and supraphysiological conditions and to be similar to those previously used in human [18F]FDG-PET studies.


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Subjects and study design. We studied 18 normal male subjects who were randomly assigned to three groups. One group of subjects was studied after an overnight fast, one under physiological, and one under supraphysiological (pharmacological) hyperinsulinemic-euglycemic conditions. The subjects were healthy, as judged by history, physical examination, and routine laboratory tests and were not taking any medications. Physical characteristics of the subjects are shown in Table 1. Written informed consent was obtained after the purpose, nature, and potential risks were explained to the subjects. The experimental protocol was reviewed and approved by the Ethics Committee of the Department of Medicine, Helsinki University Central Hospital.

                              
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Table 1.   Physical characteristics of the subjects

Whole body glucose uptake. Whole body glucose uptake was quantitated by use of the euglycemic-hyperinsulinemic clamp technique (8). Serum insulin was increased to a predetermined level by means of a primed continuous insulin infusion (Actrapid Human, Novo Nordisk, Copenhagen, Denmark) at rates of either 1 (physiological) or 5 (supraphysiological) mU · kg-1 · min-1. Insulin was infused in an antecubital vein, and the duration of insulin infusion was 180 min. Normoglycemia was maintained by adjusting the rate of a 20% glucose infusion (Glucosteril, Orion, Espoo, Finland) based on plasma glucose measurements performed at 5- to 10-min intervals. Blood samples for the measurement of plasma glucose concentrations were taken from a heated dorsal hand vein. Because hepatic glucose production is completely suppressed during 1-5 mU · kg-1 · min-1 insulin infusions in normal subjects (21, 24), whole body glucose uptake was calculated from the glucose infusion rate after correction for changes in the glucose pool size (8). Blood samples were taken at 30-min intervals for measurement of the serum-free insulin concentrations.

Forearm glucose uptake. Forearm blood flow was measured by venous occlusion plethysmography using mercury in Silastic rubber strain gauge apparatus (Hokanson Plethysmograph Model EC4, Bellevue, WA), as previously described in detail (42). Forearm glucose uptake was calculated with the Fick principle by multiplying the blood glucose arteriovenous difference by the forearm blood flow.

Determination of the LC. The triple tracer technique has been used to examine transmembrane glucose transport and intracellular glucose phosphorylation in human forearm muscle (1, 6, 39). The modification of the technique used in the present study involves the simultaneous intrabrachial injection of an extracellular tracer (mannitol), a glucose tracer that behaves like glucose {D-[3-3H]glucose [3H]Glc} (45), and the glucose analog for which the LC is determined (2-[1-14C]DG) and measurement of tracer concentrations in deep venous blood. A 27-gauge needle (Cooper's Needle Works, Birmingham, UK) was inserted into the brachial artery, and a bolus (total volume ~200 µl) containing ~60 µmol [12C]mannitol (150 mg/ml, Pharmacia, Stockholm, Sweden), ~190 kBq [3H]Glc (Amersham TRK239), and ~150 kBq 2-[1-14C]DG (Amersham CFA.562) was rapidly injected intrabrachially. Blood samples were drawn frequently (every 6-30 s) from the deep forearm vein for 15 min for the determination of tracer concentrations in the venous effluent. Suprasystolic pressure was applied to a wrist cuff during the bolus injection and blood collection. Because forearm blood flow is only ~1% of cardiac output, recirculation of any substance injected into the brachial artery is negligible (6, 39). The bolus was injected after 165 min of insulin infusion. An example of washout curves of the three tracers is shown in Fig. 1.


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Fig. 1.   Example of the washout curves of the 3 tracers. Man, [12C]mannitol; 3-[3H]-Glc, [3-3H]glucose; 1-[14C]-2-DG, 2-deoxy-[1-14C]glucose. The dots denote the measured data of one of the subjects studied under hyperinsulinemic conditions.

Calculation of the LC. The LC is by definition the ratio between the extraction (E) of 2-[1-14C]DG and [3H]Glc
LC<IT>=</IT><FR><NU>E<SUP>2-DG</SUP></NU><DE>E<SUP>[<SUP>3</SUP>H]Glc</SUP></DE></FR><IT>=</IT><FR><NU>CR<SUP>2-DG</SUP>/F</NU><DE>CR<SUP>[<SUP>3</SUP>H]Glc</SUP>/F</DE></FR> (1)
where CR denotes the clearance rate and F the blood flow. The method developed for the calculation of the LC is virtually model independent and is based on the following considerations. The fractional extraction of a generic metabolizable tracer, e.g., 2-DG or [3H]Glc (denoted below with *) in a bolus injection experiment can be expressed as [see, e.g., (47)]
E*<IT>=</IT><FR><NU>CR*</NU><DE>F</DE></FR><IT>=1−</IT><FR><NU><LIM><OP>∫</OP><LL><IT>0</IT></LL><UL><IT>∞</IT></UL></LIM> C<SUP>*</SUP><SUB>V</SUB>(<IT>t</IT>)dt</NU><DE><LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> C<SUP>*</SUP><SUB>A</SUB>(<IT>t</IT>)dt</DE></FR> (2)
where C*A and C*V are the dose-normalized arterial and venous whole blood tracer concentrations, respectively, and the assumption is made that the tracer uptake (U*) is U*(t) = CR* × C*A(t). In the absence of tracer recirculation [a valid assumption for forearm skeletal muscle (6, 39)], one also has
<LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> C<SUP>*</SUP><SUB>A</SUB>(<IT>t</IT>)d<IT>t=1/</IT>F (3)
F can easily be determined by resorting to a nonmetabolizable tracer like mannitol
F<IT>=1/</IT><LIM><OP>∫</OP><LL><IT>0</IT></LL><UL><IT>∞</IT></UL></LIM> C<SUP>Man</SUP><SUB>V</SUB>(<IT>t</IT>)d<IT>t</IT> (4)
where CVMAN denotes the dose-normalized venous whole blood concentration of mannitol.

By substituting Eqs. 3 and 4 into Eq. 2, one can see that the LC of Eq. 1 is given by
(5)
The concentrations appearing in Eq. 5 are whole blood venous concentrations and have been obtained from the measured plasma concentrations as [see, e.g., (6, 39)]
C<SUP>Man</SUP><SUB>V</SUB>(<IT>t</IT>)<IT>=</IT>(<IT>1−</IT>H)C<SUP>Man</SUP><SUB>VP</SUB>(<IT>t</IT>) (6)

C<SUP>2-DG</SUP><SUB>V</SUB>(<IT>t</IT>)<IT>=</IT>(<IT>1−0.3</IT>xH)C<SUP>2-DG</SUP><SUB>VP</SUB>(<IT>t</IT>) (7)

C<SUP>[<SUP>3</SUP>H]Glc</SUP><SUB>V</SUB>(<IT>t</IT>)<IT>=</IT>(<IT>1−0.3</IT>xH)C<SUP>[<SUP>3</SUP>H]Glc</SUP><SUB>VP</SUB> (8)
where H is the hematocrit and suffix P denotes plasma. The factor 0.3 was derived from the equation developed and validated by Dillon (10) and assumes the water content of red cells and plasma to be 65 and 93%, respectively. The area under the concentration curves of Eqs. 6-8 was calculated by use of linear interpolation and the trapezoidal rule in the experimental period (15 min) and by use of a monoexponential model to extrapolate the data to infinity. Parameters of the monoexponential model were estimated by weighted nonlinear least squares (5).

Analytical methods. To determine plasma concentrations of [3H]Glc and 2-[1-14C]DG in the deep venous effluent, plasma was precipitated with Ba(OH)2 and ZnSO4 (44). Aliquots of the supernatant were evaporated to dryness, reconstituted with water, mixed with scintillation fluid, and counted for 3H and 14C radioactivity in a two-channel liquid scintillation counter (Wallac 1409, Wallac, Turku, Finland). Mannitol isotopic enrichment was determined by gas chromatography-mass spectrophotometry as previously described (2). The plasma glucose concentration was measured in duplicate by the glucose oxidase method (20) with the use of the Beckman Glucose Analyzer II (Beckman Instruments, Fullerton, CA). Serum-free insulin concentrations were determined by double antibody RIA (Insulin RIA kit, Pharmacia, Uppsala, Sweden) after precipitation with polyethylene glycol (9).

Other measurements. The percentage of body fat was determined by bioelectrical impedance analysis (BioElectrical Impedance Analyzer System model no. BIA-101A, RJL Systems, Detroit, MI).

Statistical analyses. Group comparisons were performed with the one-way analysis of variance followed by the unpaired Student's t-test and the Bonferroni correction for pairwise comparisons. Simple linear regression analysis was used to determine the relationship between LC and various parameters. All statistical analyses were performed with the SYSTAT software (Systat, Evanston, IL). The results are expressed as means ± SE. P values <0.05 were considered statistically significant.


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Plasma glucose and serum insulin concentrations and whole body and forearm glucose uptake. Serum insulin concentrations averaged 29 ± 8 pmol/l in the basal study and 445 ± 28 and 2,404 ± 123 pmol/l during the 1 and 5 mU · kg-1 · min-1 insulin infusions, respectively (P < 0.001 for all comparisons). Plasma glucose concentrations averaged 5.3 ± 0.1, 5.1 ± 0.1, and 5.2 ± 0.1 mmol/l, respectively (NS). The rates of whole body (64 ± 8 µmol · kg body wt-1 · min-1) and forearm (5.5 ± 0.6 µmol · dl forearm-1 · min-1) glucose uptake were higher during the 5 mU · kg-1 · min-1 insulin infusion than during the 1 mU · kg-1 · min-1 insulin infusion (41 ± 3 µmol · kg body wt-1 · min-1, 3.8 ± 0.5 µmol · dl forearm-1 · min-1, respectively; P < 0.05 for both 1 and 5 mU · kg-1 · min-1).

Lumped constant. The LC averaged 1.26 ± 0.08 (range 1.06-1.43), 1.15 ± 0.05 (0.99-1.39), and 1.18 ± 0.05 (0.97-1.37) in the basal state and during the 1 and 5 mU · kg-1 · min-1 insulin infusions, respectively (NS). Individual data are shown in Table 2. No significant associations were found between the LC and serum insulin concentrations (r = 0.16 for pooled data, NS), rates of whole body (r = -0.04, NS) or forearm (r = -0.10, NS) glucose uptake, or with physical characteristics such as body mass index or the percentage of body fat (data not shown).

                              
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Table 2.   Extraction of 2-[1-14C]DG and [3H]Glc, calculated blood flow, and LC at various insulin infusion rates


    DISCUSSION
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In the present study, we directly measured the LC for 2-DG in vivo in human skeletal muscle. We observed that the LC 1) is constant over a wide range of insulin concentrations (29-2,400 pmol/l), 2) is not dependent on the rate of insulin-stimulated glucose uptake, and 3) averages 1.2. Our study confirms that 2-DG (and possibly also [18F]FDG) can be used not only as a qualitative but also as a quantitative glucose tracer analog to examine skeletal muscle glucose utilization in humans. In keeping with this, we had previously observed a very close and similar relationship between femoral muscle glucose uptake measured with [18F]FDG-PET and whole body glucose uptake measured by the euglycemic clamp technique. This relationship was found in both women and men (31), in patients with insulin-dependent diabetes mellitus (32), in athletes (30), and at various free fatty acid concentrations (33). In addition, when muscle glucose uptake was measured in comparable groups of normal subjects by use of the forearm balance (46) and the [18F]FDG-PET techniques (assuming an LC of 1.0), remarkably similar rates of glucose uptake were found (33). The present study, however, suggests that the rate of muscle glucose uptake may have been slightly (~20%) overestimated in the previous studies by us (30, 31, 32, 33) and others (22, 34, 40).

[18F]FDG is a labeled glucose analog in which the hydrogen in the 2-position is replaced by 18F. Because fluorine is only slightly larger (van der Waals radius 1.35 Å) than hydrogen (1.20 Å), the introduction of a fluorine atom into a non-fluorine-containing deoxyglucose does not cause any steric changes. The low positron energy (0.64 MeV) results in low radiation doses and short ranges in tissues (<2.4 mm) (17). The half-life of [18F]FDG (109.8 min) permits scanning procedures and metabolite analyses extending over hours, thus facilitating kinetic studies. Intracellularly, [18F]FDG is phosphorylated by hexokinase. As glucose 6-phosphatase activity in skeletal muscle is negligible, [18F]FDG is efficiently metabolically trapped within the muscle cell. Thus [18F]FDG appears to be an ideal glucose tracer for PET studies. In the present set of studies, it was more practical to use the 2-[1-14C]DG analog than [18F]FDG because of the longer half-life of 14C (5,730 yr) than 18F (109.8 min). However, because glucose and [18F]FDG are more similar structurally than glucose and either the 2-[1-3H]DG or 2-[1-14C]DG used in previous studies in rats (4, 14), the LC for [18F]FDG should be closer to unity than that of 3H- or 14C-labeled glucose analogs (27).

In human skeletal muscle, regulation of glucose phosphorylation by insulin is complex because it involves different hexokinase isoforms and changes in the subcellular localization of hexokinase II in response to insulin (43). Both of these factors could influence their affinity for glucose relative to 2-DG, as may (38) or may not (11) be the case in the heart. Assuming that the relative rates of glucose transport and phosphorylation are the major determinants of the LC, the LC could be regarded as a macroscopic correction factor for both of these processes. Considering that the affinity [Michaelis-Menten constant (Km)] of hexokinase for glucose in cultured human skeletal muscle cells and in rat skeletal muscle is 4- to 10-fold higher than that of 2-DG (7, 16, 19), the finding of an LC slightly greater than 1 suggests, in view of similar Km of glucose and 2-DG for glucose carriers (7, 19, 23), that glucose transport, rather than phosphorylation, was rate limiting under all experimental conditions in the present studies. Of note, all concentrations in Eq. 5 (LC) were whole blood concentrations, which were calculated from measured plasma concentrations on the assumption that the relationships for glucose could be applied to 2-DG. Because the Km of the glucose transporter for glucose seems close to that of 2-DG (7, 19, 23), and because the erythrocyte glucose transporter GLUT-1 (28) is not insulin sensitive, this assumption does not invalidate the conclusion that the LC for 2-DG is similar under basal and insulin-stimulated conditions.

Regarding calculation of regional glucose uptake rates with the use of the Sokoloff model (41) and the graphic analysis method of Patlak and Blasberg (35), the present data merely demonstrate that, at least in normal subjects, in skeletal muscle the same LC can be used under both basal and hyperinsulinemic conditions. The present data do not, however, validate the quantitation of rates of glucose transport and phosphorylation with the Sokoloff or any other model.

The present data showing no effect of insulin on the LC in skeletal muscle do not necessarily apply to the myocardium. Studies performed in the isolated perfused working rat heart preparation have suggested that the LC may be dependent on the insulin concentration in the perfusate (18) or substrate concentrations such as the availability of lactate or ketone bodies (18) or free fatty acids (12), as well as oxygen availability (12). It is, however, difficult to extrapolate the data obtained in animal studies (ex vivo) to humans, because there may be differences related to the experimental preparation or the species. For example, insulin increases myocardial glucose and 2-DG uptake in the isolated rat heart preparation (18) much less than it does in humans in vivo (3, 13, 26). Also, recent studies examining myocardial kinetics of [18F]FDG in human subjects showed [18F]FDG to quantitatively trace glucose uptake both basally (LC = 1.44) and during insulin infusion (LC = 0.99) (29).

In conclusion, in normal subjects, the lumped constant for 2-DG in human skeletal muscle is constant over a wide range of insulin concentrations and averages 1.2. These data support the use of 2-DG analogs in the quantitation of regional glucose uptake in human skeletal muscle. However, because glucose transporters and hexokinases differentiate between 2-DG and native glucose, these data also imply that only the total rate of glucose uptake, and not necessarily the rates of glucose transport or phosphorylation, can be measured with a single glucose tracer analog.


    ACKNOWLEDGEMENTS

We are grateful to Riccardo Bonadonna from the University of Verona for help and valuable comments. We thank Sari Haapanen and Kati Tuomola for skillful technical assistance.


    FOOTNOTES

This study was supported by grants from the Academy of Finland (H. Yki-Järvinen), the Foundation for Diabetes Research (T. Utriainen), the Finnish Medical Foundation (T. Utriainen), and the M.D./Ph.D. Program of the University of Helsinki (T. Utriainen).

Address for reprint requests and other correspondence: H. Yki-Järvinen, Dept. of Medicine, Div. of Diabetology, Univ. of Helsinki, PO Box 340, Haartmaninkatu 4, FIN-00029 HUCH, Helsinki, Finland (E-mail: ykijarvi{at}helsinki.fi).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.

Received 24 June 1999; accepted in final form 24 February 2000.


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ABSTRACT
INTRODUCTION
SUBJECTS AND METHODS
RESULTS
DISCUSSION
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