SPECIAL COMMUNICATION
Determination of cerebral glucose transport and metabolic kinetics
by dynamic MR spectroscopy
P. C. M.
Van Zijl1,
D.
Davis1,
S. M.
Eleff1,2,
C. T. W.
Moonen3,
R. J.
Parker4, and
J. M.
Strong4
Johns Hopkins University Medical School, Departments of
1 Radiology and
2 Anesthesiology and Critical
Care, Baltimore 21205; 3 National
Institutes of Health, In Vivo Nuclear Magnetic Resonance Research
Center, Biomedical Engineering and Instrumentation Program, National
Center for Research Resources, Bethesda 20892;
4 Food and Drug Administration,
Center for Drug Evaluation and Research, Office of Research Resources,
Division of Clinical Pharmacology, Rockville, Maryland 20850; and
3 Resonance Magnetique des
Systemes Biologique, Unité Mixte de Recherche 5536, Centre
National de la Recherche Scientifique, Université Victor
Segalen 2, F-33076 Bordeaux Cedex, France
 |
ABSTRACT |
A new in vivo nuclear magnetic resonance (NMR)
spectroscopy method is introduced that dynamically measures cerebral
utilization of magnetically labeled
[1-13C]glucose from
the change in total brain glucose signals on infusion. Kinetic
equations are derived using a four-compartment model incorporating glucose transport and phosphorylation. Brain extract data show that the
glucose 6-phosphate concentration is negligible relative to
glucose, simplifying the kinetics to three compartments and allowing
direct determination of the glucose-utilization half-life time
[t1/2 =
ln2/(k2 + k3)] from
the time dependence of the NMR signal. Results on isofluorane
(n = 5)- and halothane
(n = 7)- anesthetized cats give a
hyperglycemic
t1/2 = 5.10 ± 0.11 min
1 (SE). Using
Michaelis-Menten kinetics and an assumed half-saturation constant
Kt = 5 ± 1 mM, we determined a maximal transport rate Tmax = 0.83 ± 0.19 µmol · g
1 · min
1,
a cerebral metabolic rate of glucose
CMRGlc = 0.22 ± 0.03 µmol · g
1 · min
1,
and a normoglycemic cerebral influx rate
CIRGlc = 0.37 ± 0.05 µmol · g
1 · min
1.
Possible extension of this approach to positron emission tomography and
proton NMR is discussed.
[13C]glucose
utilization; brain; Michaelis-Menten kinetics; cat; nuclear magnetic
resonance spectroscopy
 |
INTRODUCTION |
GLUCOSE IS THE PRIMARY fuel for energy metabolism in
normal brain, and the availability of noninvasive in vivo methods for the elucidation of its transport and metabolic kinetics should be
important in the study of a multitude of brain disorders (17, 21). An
ideal method for measuring cerebral rates of influx (CIRGlc) and metabolism (CMRGlc) should allow
direct monitoring of the separate processes of tissue uptake and
utilization of glucose under physiological conditions. At present, the
most sensitive in vivo approach is the use of radiolabels, which can be
applied in tracer amounts (9, 10, 14, 23, 26, 27). However, the
interpretation of these measurements is complicated by the fact that
the sum of all radiolabels, which basically includes all metabolic
products, is measured (13). This problem has been addressed by using
glucose derivatives that are trapped after phosphorylation, e.g.,
deoxyglucose analogs (14, 26, 27), but these compounds may differ in
their transport and utilization properties with respect to glucose.
This difference is generally accounted for empirically by the use of
so-called lumped constants in positron emission tomography (PET) (7,
22). It has been suggested that the kinetic equations for deoxyglucose
may need to account for the potentially reversible character of
saturable phosphorylation (14), but irreversibility is generally used as a reasonable assumption.
An alternative approach that can be applied to study glucose
utilization without the need for a lumped constant is the nuclear magnetic resonance (NMR) study of nonradioactive magnetically labeled
glucose, e.g., the naturally occurring isotopomer
[1-13C]glucose (3, 4,
11, 30). In principle, NMR can study both the uptake (influx) and
metabolism of
[1-13C]glucose (11,
18, 30), because different metabolites labeled in different carbon
positions generally result in different NMR spectral frequencies
(chemical shifts). This specific labeling has been studied by
13C NMR in animals and humans (2,
4, 11). Indirect determination of transport kinetics was recently also
achieved by applying equilibrium Michaelis-Menten kinetics to the
experimentally measured ratios of plasma and tissue glucose (11).
However, NMR is an insensitive method with several inherent problems
that interfere with optimum use of its enormous potential. For
instance, the time necessary to acquire a
13C NMR spectrum is much longer
than the typical time constant for glucose uptake and phosphorylation,
thereby prohibiting direct kinetic determination of the rates of
glucose influx and utilization. The sensitivity of
13C NMR can be improved by
detecting the proton nuclei coupled to the labeled carbon nuclei (8,
24), but until recently this approach prohibited detection of
[1-13C]glucose due to
its overlap with the dominant water resonance (108 M proton
concentration due to 2 protons/water molecule vs. millimolar
concentration for the glucose). Therefore, this
[1-13C]glucose
transport step has not yet been studied dynamically by
13C NMR, and assumptions for this
part of the metabolic process have to be made when formation of
[13C]glutamate (18)
and [13C]lactate (25)
is studied. We have recently developed proton NMR methods that can
simultaneously detect all metabolites, even when they are resonating at
the same frequency as water (29), and we apply this method here to
dynamically study uptake and metabolism of
[1-13C]glucose in
healthy cat brain. This approach is the closest possible NMR analog
of a PET experiment, since we can limit the detected signal
to consist of glucose and phosphorylated glucose only. NMR is not able
to use fluorodeoxyglucose due to its toxicity when used in
the amounts required for NMR (5).
Glossary
BBB |
Blood-brain barrier
|
CP,
,
CtotP |
Unlabeled (12C), labeled (13C), and total
plasma glucose concentrations (mM)
|
CE, ,
CtotE |
Unlabeled, labeled, and total tissue glucose concentrations (mM)
|
CM, ,
CtotM |
Unlabeled, labeled, and total phosphorylated glucose concentrations in
brain tissue (mM)
|
Ci |
Sum of phosphorylated and tissue glucose concentrations (mM)
|
CGlc |
Total concentration of glucoses (mM): CGlc = CP + CE + CM
|
Cblood |
Arterial blood glucose concentration (mg/dl)
|
CX,eq |
Concentrations at equilibrium
|
CMRGlc |
Cerebral metabolic rate of glucose
(µmol · g 1 · min 1)
|
CIRGlc |
Cerebral influx rate of glucose (µmol · g 1 · min 1)
|
fvas |
Vascular volume fraction
|
GC-MS |
Gas chromatography-mass spectroscopy
|
Hct |
Hematocrit
|
HMQC |
Heteronuclear multiple quantum coherence
|
Kt |
Michaelis-Menten half-saturation constant (mM) for glucose transport
|
Khaset |
Michaelis-Menten half-saturation constant for glucose phosphorylation
(hexokinase-catalyzed = hase)
|
k1 |
Rate constant for glucose influx in the brain
(min 1)
|
k2 |
Rate constant for glucose efflux from the brain
(min 1)
|
k3 |
Rate constant for glucose phosphorylation in brain tissue
(min 1)
|
k4 |
Rate constant for hydrolysis (dephosphorylation) of glucose phosphate
(min 1)
|
k5 |
Rate constant for metabolism of glucose phosphate
(min 1)
|
MRS |
Magnetic resonance spectroscopy
|
MRI |
Magnetic resonance imaging
|
NMR |
Nuclear magnetic resonance
|
PET |
Positron emission tomography
|
Tmax |
Michaelis-Menten maximum transport rate of glucose
(µmol · g 1 · min 1)
|
T0 |
Time necessary for labeled glucose to reach brain after start of
infusion (min)
|
t1/2 |
Half-life time for glucose utilization
[ln2/(k2 + k3)]
|
Vd |
Whole brain water volume (ml/g)
|
 |
MATERIALS AND METHODS |
Metabolic model.
The model presented here is based on Sokoloff's
[14C]deoxyglucose
model (14, 27) developed for autoradiography. It is extended to include
the specific assumptions necessary for our NMR experiments. For
instance, although tracer kinetics do not apply, it is assumed that
first-order kinetics are still valid because the observed processes are
unsaturable. Second,
[1-13C]glucose is a
naturally occurring isotopomer of glucose, and it is generally assumed
that the kinetic constants are the same as for the nonmagnetic
isotopomer
[12C]glucose, thereby
avoiding the need for a lumped constant. We would like to point out
that this assumption is not trivial, because atoms of different weight
and different size react equivalently chemically, but may do so at a
different rate. This effect is actually used by archaeologists to study
evolution from the behavior of carbon isotopes during photosynthesis
(for a review of this literature see Ref. 28). However, although this
effect is significant (a few percent) for
CO2 fixation, it is expected to be
negligible for the glucose transport and metabolism steps studied here.
The reasons are that the bond to the isotope is not broken and that the
change from 12C to
13C should not influence the size
(M = 181) and shape of the glucose unit significantly for an enzyme to distinguish between the two isotopes. Thus the general assumption in NMR and PET that isotopic labeling of a single carbon atom does not influence the enzyme kinetics
of transport and metabolism is very plausible.
To describe the experiment completely, the model needs four
compartments (Fig. 1), namely a blood
compartment, a compartment for glucose in tissue, a compartment for
phosphorylated glucose in tissue, and a compartment for metabolic
products synthetized after phosphorylation. The boundary between the
first two compartments consists of the capillary and cell membranes
(BBB). Following Sokoloff et al. (26, 27), the capillary
glucose concentration will be approximated by the arterial plasma
glucose concentration. With the assumption of rapid equilibration of
glucose over the cell membranes (1, 17) or, equivalently for the model,
visualizing the capillary and cell membrane as a single barrier, the
next boundary is the hexokinase-catalyzed phosphorylation of glucose. Because the
[13C]glucose
utilization is not saturable, it is not necessary to include the effect
of hydrolysis of phosphorylated glucose back to glucose, and it is
accurate to assume a zero rate constant k4 for
this step. To account for efflux of phosphorylated glucose into
different products, a fourth compartment is introduced, described by
the single rate constant k5. This approach is
supported by data from direct 13C
NMR spectroscopy at equilibrium (2, 4), which show that the
concentrations of any intermediates between total
[1-13C]glucose and
[4-13C]glutamate are
negligible, indicating rapid conversion to each next step. Thus
consecutive metabolism after phosphorylated glucose in healthy brain
can be described by a single rate constant
k5 to
[4-13C]glutamate. In
this respect, it is important to notice that it is indifferent for our
model if the step to the first product after phosphorylated glucose is
rate determining or if the last step (conversion to glutamate) is.

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Fig. 1.
Metabolic model for glucose uptake, phosphorylation and subsequent
metabolism in brain. BBB, blood-brain barrier (capillary membrane) and
other potential barriers to uptake in tissue. Glucose-6-P,
glucose 6-phosphate. Rate constants k and concentrations C
are defined in Glossary. Due to unsaturable character of
metabolism, rate constant
k4 can be
neglected. In our proton-detected 13C NMR experiments (Fig.
2) we measure total of plasma and tissue
[1-13C]glucose contributions
(Eq. 7 ).
|
|
Following Sokoloff et al. (27), the concentrations of
glucose in blood plasma and tissue are denoted by
CP and
CE, whereas the concentration of
phosphorylated glucose is given by
CM. Total tissue glucose is
Ci. All compartments contain
normal and 13C-enriched compounds,
whereby enrichment is denoted by an asterisk (*). Care has to be taken
in deriving the rate equations, since the rates are determined by the
total glucose concentrations (labeled + unlabeled, e.g.,
CtotP = CP +
), whereas only changes in the
labeled compounds are measured by our proton-detected 13C NMR spectroscopy method. To
account for this, our equations are derived with the assumption that
the unlabeled glucose concentration remains constant during the short
experiment. We have confirmed this assumption for the blood compartment
using GC-MS (see RESULTS). With the
assumption that hyperglycemia (20-30 mM glucose) does not alter
the steady-state transport and metabolism of glucose and using the fact
that the concentration of unlabeled glucose is constant, the rates of
change of
CtotE(t)
and
CtotM(t) are given by
|
(1)
|
|
(2)
|
The solution to Eq.
1 for the tissue concentration of
labeled glucose at time T after
introduction of
[1-13C]glucose into
the blood is
|
(3)
|
In
our [1-13C]glucose
infusion protocol, we rapidly (within 0.5-2 min) raise the total
plasma glucose concentration (CtotP = CP +
) to the desired hyperglycemic
level (20-30 mM) and keep it constant (at equilibrium) for the
remainder of the experiment. Thus the concentration of labeled glucose
can be taken constant at any point in time, and
(t) =
. The integral in
Eq. 3
can then be evaluated for any time T
|
(4)
|
Analogously
to Eqs.
1 and 3, the solution for the concentration
of phosphorylated glucose at any time point
T is given by
|
(5)
|
Substitution
of Eq.
4 into
Eq.
5, evaluation of the integral and
rearrangement of the expression in terms of a common denominator leads
to the following result
|
(6)
|
Although most compounds detected by NMR have different
chemical shifts in the proton or carbon frequency range, spectral resolution does not allow in vivo separation of the signals of blood
and tissue glucose and glucose 6-phosphate
(G-6-P). Thus the operational
equations have to describe the concentration
, which is the sum of the
contributions of labeled tissue glucose and
G-6-P
(
) and labeled plasma glucose,
corrected for the vascular-tissue volume fraction
fvas
|
(7)
|
Finally, to describe the change of the labeled tissue plus
plasma glucose,
, as a
function of time from the start of infusion to equilibrium, the
expressions at equilibrium (
/dt =
/dt = 0) have to be evaluated. Combination of
Eqs.
1, 2,
and 7 leads to the following two
expressions at equilibrium
|
(8a)
|
|
(8b)
|
The complete expression describing the combined changes of
glucose in plasma and tissue plus
G-6-P in tissue can be obtained from
combining Eqs.
4, 6,
7, and
8
|
(9a)
|
In this equation a correction time delay
T0 has been added
to adjust for the delay time between the start of the infusion and the
time that glucose reaches the brain, which basically is the intercept
of the experimental curve with the time axis.
Equation 9a shows that the experimental curve
can be fitted independently of knowledge of the actual plasma and
tissue glucose concentrations by calibrating the signal intensities
with respect to the signal intensity at equilibrium. The curve has to
be fitted to four rate constants. The time intercept
T0 is well known
from the experimental arterial plasma data and is not an additional
variable. If the plasma contribution to the spectrum can be neglected
(fvas = 0), the curve
represents the combined tissue glucoses and has to be fitted to only
three rate constants
|
(9b)
|
Equations
9a and 9b are the exact operational equations
to be used for fitting the experimental data to a four-compartment model. A quick check of their accuracy is provided by calculating the
limit for equilibrium between inflow and metabolism: for long times
T, all rate constants and vascular
fractions drop out.
Determination of rate constants from the proton-detected
13C NMR spectra.
To obtain the rate constants and
T0, the
experimental glucose uptake and phosphorylation curve has to be fitted
to Eq.
9a or 9b. Fitting of a single experimental
curve to three or four rate constants may lead to a large variance in
the results. This variance can be reduced if additional restrictions
and/or reasonable starting values are available for the
variables. To simplify the problem, it would be very convenient to know
the concentration of phosphorylated glucose. We therefore measured
in extracts of in vivo
brain (see RESULTS) and found it to
be negligible compared with labeled tissue glucose. As a consequence,
the kinetic model can be reduced to three compartments analogously to
the unsaturated PET experiment described by Sokoloff et al. (27), and
the process can be described by rate constants
k1-k3.
The relevant Eqs.
7, 8b, and
9b then reduce to
|
(10)
|
|
(11)
|
|
(12)
|
The above equations describe the rate equations for labeled
glucose only, which apply to our present method for gradient-enhanced proton-detected 13C spectroscopy
in which we only detect compounds that have one or more protons
directly connected to a labeled carbon nucleus. However, it should
still be shown that we detect
[1-13C]glucose only
and not any other metabolites. As mentioned, most compounds detected by
NMR spectroscopy have different chemical shifts in the proton or carbon
frequency range and can be detected separately (30). Although spectral
resolution does not allow in vivo separation of the signals of blood
and tissue
[1-13C]glucose and
[1-13C]G-6-P,
the total glucose signals (4.6 and 5.4 ppm) can be separated from all
other brain metabolic glucose products that are present in sufficient
concentration during our 30- to 40-min experiment (Fig.
2). First of all, the metabolic products in
the subsequent series of reactions from phosphorylated glucose to
pyruvate do not have protons connected to
13C and are therefore not
detected. Second,
[3-13C]pyruvate has
the proton resonance at 2.4 ppm and its
13C resonance at 28.5 ppm. The
first experimental (Fig. 2) proton signal appearing in addition to the
total glucose resonances in healthy brain is at 2.4 ppm and could in
principle be
[3-13C]pyruvate (15)
or
[4-13C]glutamate-glutamine
(24, 29). As mentioned above, combined proton and carbon studies have
shown the first detectable product to be
[4-13C]glutamate (2,
4, 8, 29). Thus our experiment measures total labeled glucose:
(T).

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Fig. 2.
A: proton-detected
13C spectra (each spectrum 1 min
24 s) showing spectral changes during infusion. All spectra are
difference spectra with respect to preinfusion. Infusion was started
after the 4th displayed spectrum. Resonances at 5.4 and 4.6 ppm are for
- and -isomers of
[1-13C]glucose,
respectively. Each signal is a doublet (170 Hz splitting). The very
small signals just appearing at 2.4 ppm are from 1st metabolic product,
[4-13C]glutamate. For
experiment we use total glucose signal.
B: comparison of normalized (with
respect to equilibrium: 100%), total arterial glucose levels ( ) and
spectral glucose intensities ( ). C:
brain glucose uptake curve in concentration units, determined using the
procedure outlined in MATERIALS AND
METHODS. Result of data fitting to
Eq.
12 and dashed line used to determine
k1 from initial
rate are also displayed.
|
|
Two cases can now be distinguished, one in which data interpretation is
straightforward and one requiring an additional assumption. If the
vascular contribution is negligible, spectral intensities can be scaled
with respect to the equilibrium spectral intensities and the resulting
exponential can be fitted to Eq.
12, allowing direct determination of
the tissue glucose half-life time without additional assumptions
|
(13)
|
If the vascular contribution is not negligible, the
experimental NMR signal intensities represent
(T)
in Eq. 10, and, to obtain the corresponding
(T)
in each point, the data have to be corrected. This can be done by using
Eq.
10 to calculate
from the equilibrium
ratio of plasma and tissue glucose reported in the literature and the experimentally determined plasma level for labeled glucose
. After the
C* Glc(T ) curve is
normalized with respect to
, the correct
(T)
values can be obtained using Eq. 10 and the experimental
(T)
values. The final
(T) curve can then be fitted to Eq.
12. In
RESULTS and
DISCUSSION, we will evaluate the
influence of the vascular contribution on the final rate constants. The
tissue-to-plasma glucose ratio at equilibrium has been determined for
rats with the use of rapidly frozen brains (19, 22) and in humans with
the use of 13C NMR spectroscopy
(11). In the following we neglect the phosphorylated glucose
contribution in the notation, as warranted by the experimental results.
The animal studies, which report plasma glucose in millimolar units and
tissue glucose in micromoles per gram wet weight, give CtotE, eq/CtotP, eq =
/
= 0.27-0.28 ml/g (19) and 0.33 ml/g (22). With the use of an
average of 0.30 ml/g and a whole brain water volume
Vd = 0.77 ml/g (6), this is
equivalent to
/
= 0.77/0.30 = 2.6. The human NMR studies, measuring plasma and tissue
concentrations in millimolar units, show a concentration dependence of
/
,
with values ranging from 3.2 to 4.0 for the concentration range in our
experiments. Data from PET and autoradiography have also provided plasma-to-tissue ratios for glucose in this same range. In the present
study we therefore evaluate a range of
/
values between 1.6 and 3.6 for calculating the rates of transport and
metabolism. For completeness, it may be of interest to note that, for
cases in which the phosphorylated glucose concentration would be
important, addition of the plasma-to-tissue ratio reduces the number of
unknowns in Eq.
9a to three but does not reduce the number of unknowns in Eq.
9b. As a matter of fact,
Eqs.
9a and 9b become equal if
Eq. 7
is used to correct the experimental data for the assumed
tissue-to-plasma ratio and the vascular volume.
Finally, once the tissue glucose turnover rate
(k2 + k3) is
determined, the rate constant
k1 can be
calculated from Eq.
11. Another approach of determining
k1 is by initial
rate determination using the initial slope (time derivative of the
early points) of the experimentally determined
(T)
curve. Assuming no phosphorylation or efflux in the early minutes, the
working equation for initial rate experiments can be derived from
|
(14)
|
The
solution for this equation is
|
(15)
|
For
our case of negligible phosphorylation, we determine
k1 both from
Eq.
11 and from the initial rate
approximation and compare the results and accuracies for different
vascular fractions and plasma-to-tissue ratios. In the general case
including phosphorylation, determination of
k1 by the initial
rate approach reduces the situation to two equations
(Eqs.
8b and 9b) and three unknowns, which may in
some cases be fitted accurately.
At equilibrium, the rate constants are related to the glucose influx
(CIRGlc) and utilization
(CMRGlc) rates in micromoles per
gram per minute by
|
(16)
|
|
(17)
|
These
parameters, describing the facilitated inflow of glucose and its
metabolism, respectively, are equivalent to the quantities Vin and
Vgly used by
Mason et al. (18) in their evaluation of glutamate production by the
trichloroacetic acid cycle. Equation 17 also indicates that, in the present
model at equilibrium, the effective glucose transport rate
(k1CtotP, eq
k2CtotE, eq)
is equal to the phosphorylation rate.
Data processing protocol.
In our experiments, the NMR signal intensity of total
[1-13C]glucose and the
total arterial blood glucose concentration (glucose analyzer) are
measured as a function of time. The data are processed as follows.
1) The plasma glucose
concentrations before infusion
(CtotP = CP)
and at the plateau phase (6-10 points) of the total glucose curve
(CtotP =
+ CP) are calculated from the
experimentally determined total arterial blood glucose concentrations
(Ctotblood) and hematocrits (Hct)
|
(18)
|
in
which 18.1 is the molar mass of
[1-13C]glucose divided
by 10 to correct for the l/dl conversion. These concentrations are then
used to determine the enriched plasma glucose concentration
at each measured time point.
2) The enriched plasma glucose level
and the rat
plasma-to-tissue ratio of glucose
(
/
= 2.6) are used to calculate the enriched tissue glucose concentration at equilibrium. The total tissue plus plasma glucose concentration in
millimolar units for the plateau phase of the curve is determined using
Eq.
10 and a specified vascular fraction.
3) The complete experimental NMR
signal intensity curve is then calibrated in terms of a
(T)
in millimolar and in terms of a
(T)
in millimolar units, as described in Determination
of rate constants from the proton-detected 13C NMR
spectra.
4) The time constant
T0 is taken as
the time that it takes for the arterial plasma levels to reach at least
65% specific activity. This determination of
T0 is accurate,
since the blood glucose rate is measured every 0.5 min in the arteries
lateral and contralateral (alternatingly) to the (femoral) infusion
vein. Thus assumption of similar plasma concentrations in the brain
arteries and these arteries seems appropriate, since all are the result
of a complete blood recirculation.
5) The rate constants and rates are determined as described
in Determination of rate constants from the
proton-detected 13C NMR spectra.
In vivo NMR measurements.
Experiments were performed on a 4.7 T GE CSI system equipped with
shielded gradients (bore size 35 cm) of up to 0.19 T/m and corrected
for additional small residual gradients by preemphasis. The so-called
gradient-enhanced HMQC pulse sequence that was used has been described
in detail elsewhere, and the parameters that were applied were exactly
as described previously (29). In short, gradient lengths were 2 ms;
postgradient delays of 300 µs were used for recovery. Additional
gradients [G(add)] of 0.06 and 0.04 T/m were used in the
z and
x directions. In some cats we used combined coherence selection gradient ratios
G1:G2:G3 = 3:5:0 and 2:2:1 in different gradient directions, which select for
the same heteronuclear coherence pathway. In other ones we only used 3:5:0 in two or three gradient directions. Variation of these selection
gradients does not influence our spectra (29). A two-step phase cycle
was used in addition to gradient selection, resulting in proton spectra
that are free of water (Fig. 2). It is important to notice that, since
only one of two coherence pathways is selected, spectra generally
cannot be phased and have to be processed as magnitude spectra.
The experimental protocol was as follows. After initial spin-echo
imaging to determine the slice position and before the start of
infusion, hardware and sequence performance were always tested on a 100 mM [1-13C]glucose
phantom placed on top of the coil. For this test, slice selection was
moved from the cat (below the coil) to the phantom. After the test,
slice position and width and proton pulse widths were optimized on the
cat brain and the slice was shimmed using the water spin echo. The
initial carbon pulse width was calculated from the in vivo proton pulse
width using the phantom proton-to-carbon pulse-width ratio. This
initial value always proved to be close to correct. Radio frequency
pulse widths generally did not vary more than 5-10% per cat
experiment. Data were processed with a line broadening of 13 Hz. In
different experiments, the number of scans acquired per spectrum varied
from 64 to 128, with different total scan times ranging between 1 and
2.5 min. Before the start of the infusion, 10-12 reference spectra
were acquired, which were later added and normalized to the intensity
of the single spectra. This reference spectrum was subtracted from the
data acquired during infusion (difference spectroscopy). The purpose of
the high number of reference spectra is to reduce signal-to-noise losses upon subtraction.
Concentric surface coils (1H
transmit/observe: 4 cm; 13C
transmit: 6 or 7.5 cm) were used together with band-pass filters. The slice selective sinc pulse (2 lobes) was 320 µs. The carbon pulses were 65-140 µs, depending on the load and available power. In most experiments no 13C decoupling
was applied.
GC-MS analysis.
Immediately after blood sampling, aliquots of 0.05 ml of arterial blood
were mixed with 0.05 ml of internal standard
D-[13C6]glucose
(5 mg/ml; 13C = 90%; Cambridge
Isotopes, Woburn, MA) and immediately frozen at
70°C. Before
GC-MS analysis, frozen blood samples were lyophilized and then
derivatized by addition of 0.1 ml of
N-trimethylsilyl imidazole (Pierce,
Rockford, IL) and 0.1 ml acetonitrile and heating in a sonicator
(Branson Instruments, Danbury, CT) at 65°C for 30 min.
Subsequently, four 1-µl aliquots of each sample were analyzed on a
HP5890/HP5971A GC-MS (Hewlett-Packard, Palo Alto, CA) equipped with a
HP-1 Column (12 m × 0.2 mm × 0.33-µm film thickness).
Injector and detector temperatures were 270 and 280°C,
respectively. The carrier gas was helium at a constant flow of 0.44 ml/min. Oven temperature stepping was programmed at 6°C/min from
160 to 250°C. Selected ions were monitored at 435 for
D-glucose, 436 for
D-[1-13C]glucose,
and 441 for
D-[1,2,3,4,5,6-13C]glucose,
with the multiplier set at 1,000 V above autotune values. From these
data,
D-glucose-to-D-[1-13C]glucose
isotope ratios were calculated. The standard curves obtained for
D-glucose and
D-[1-13C]glucose
(99% 13C) were linear over the
range of 0.5 to 4 mg/ml.
Animal preparation.
Animals were handled in accordance with the standards established by
the US Animal Welfare Acts, set forth by the National Institutes of
Health (NIH) guidelines and guidelines of the Johns Hopkins University
Animal Care and Use Committee. There were two groups of cats, namely
those studied at NIH (cats
1-5)
and those studied at Johns Hopkins University
(cats
6-12),
for which the anesthetic protocols were slightly different. Fasted cats
(adults, about 3.0 kg, either sex) were initially anesthetized with
ketamine (cats
1-5,
44 mg/kg ip) or pentobarbital sodium
(cats
6-12,
40 mg/kg ip). After tracheal intubation, the femoral arteries and veins
were catheterized. Subsequently, the animals were immobilized with 1 mg/kg succinylcholine chloride (cats
1-5,
iv) or pancuronium bromide (cats
6-12,
iv) and placed under mechanical ventilation with 1% isofluorane in
30:70%
O2-N2O
(cats
1-5)
or 0.5-1.5% halothane in oxygen-enriched air
(cats
6-12).
The tidal volume was adjusted to maintain
PaCO2 between 30 and 40 mmHg and
PaO2 >100 mmHg. Immobilization was
maintained with pancuronium bromide (0.2 mg · kg
1 · h
1).
The time between induction and the start of the infusion experiments was always at least 3 h, resulting in an anesthetic regimen of mainly
isofluorane and halothane for the two groups, respectively. Arterial pH
was maintained between 7.35 and 7.45, using sodium bicarbonate as
needed. Heart rate and blood pressure were monitored through the
femoral artery catheter. Blood gases and pH were measured with
Radiometer ABL electrodes and analyzer (Copenhagen, Denmark). Body
temperature was controlled by a thermostat-controlled water-circulated heating pad. KCL for euthanasia was administered through the femoral vein catheter. The NMR coil was placed on the head, without tissue retraction.
For the glucose uptake experiments, the blood glucose level was rapidly
increased from normal (~60-70 mg/dl = 3.3-3.9 mM) to
hyperglycemic (>250 mg/dl = 13.8 mM) within 0.5-2 min and kept constant within ~10% for the remainder of the experiment (Fig. 2B). This was achieved using an initial bolus (1.25 ml/kg)
and a subsequent infusion of exponentially decreasing rate (from 1.25 ml · kg
1 · min
1
in the first min to 0.11 ml · kg
1 · min
1
at 25 min, after which the rate was not changed) of a solution of 0.75 M [1-13C]glucose in
saline. [1-13C]glucose
(99%) was obtained from Cambridge Isotopes. Blood glucose and lactate
levels (YSI model 2300 Stat Glucose/Lactate Analyzer; Yellow Springs
Instruments, Yellow Springs, OH) were monitored by extraction of 0.2 ml
arterial blood every 0.5 min for the first 6 min of the experiment,
every 2 min for the next 6 min, and every 5-10 min at later
stages. Both remained stable within 10%. All cats studied responded
similarly to this protocol.
Extract studies.
In vivo sampling of brain tissue was performed under anesthesia.
Halothane and mechanical ventilation were continued during removal of
cats (n = 3) from the magnet after
completion of NMR experiments. The skin and muscle were incised and
reflected using electrocautery and coagulation. The bone was removed as
above, and bleeding was controlled using bone wax. The dura was
carefully reflected with a forceps and scalpel to prevent bleeding.
Brain was removed from the superficial cortex with a spatula and
rapidly frozen by pressing samples using metal tongs prepared by
submersion in liquid nitrogen. The frozen tissue was wrapped in
aluminum foil and frozen in liquid nitrogen until further processing.
The animals were then killed with potassium chloride injection.
Extracts were ground to a fine powder using a mortar and pestle cooled by immersion in liquid nitrogen. The powder was homogenized with 6%
perchloric acid using a Tekmar Tissumizer (Tekmar, Cincinnati, OH) for
3-5 min and centrifuged at 17,500 g for 15 min at 4°C. The
supernatant was neutralized with 3 M
K2CO3/1
M KOH, mixed with chelating resin (Sigma Chemical, St. Louis, MO) to
remove paramagnetic metal ion contamination, and centrifuged once more. The supernatant was freeze-dried, the lyophilized brain extract was
dissolved in D2O and filtered (0.2 µm), and the pH was adjusted to 7. High resolution proton-decoupled
13C NMR spectra of the extracts
were recorded with a Bruker MSL-500 NMR spectrometer [repetition
time: 2 or 7 s, 12 µsec (60°) pulse; sweep width 25 kHz; 32 K
data blocks zero-filled to 64 K, 2 Hz exponential line
broadening].
 |
RESULTS |
Kinetic parameters.
Figure 2A shows an example of
proton-detected
[1-13C]glucose
difference spectra acquired before and during infusion. Figure 2B compares the normalized arterial
glucose level input function (100% at equilibrium) in this cat to the
normalized changes in total proton-detected
[1-13C]glucose NMR
signal. It is clear from the difference between the two curves that the
NMR signal indeed represents brain tissue glucose input and not the
arterial glucose input. These normalized curves were first used to
determine the hyperglycemic rates
k2 + k3
(Eq.
12) and
k1
(Eq.
11) for 12 cats, assuming negligible
vascular glucose fraction (Table 1).
Subsequently, the
k2 + k3 values at
vascular fractions of 3 and 5% were determined after the total-labeled glucose curves were corrected for these plasma fractions, using the
procedure outlined in METHODS AND
MATERIALS. The results in Table 1 show that, when
normalized curves are fit,
k2 + k3 is the same
for all vascular fractions between 0 and 5%. The rate constant
k1 was determined
in two different ways, namely from k2 + k3 using
Eq.
11 and by using an initial rate
approach (Fig. 2C) in which the
tangent of the initial part of the fitted curve is determined
experimentally. The data clearly indicate that much lower (incorrect)
results are obtained for
k1 values
determined by the initial rate approach when the curve is not corrected
for the vascular fraction. This makes sense, since the largest errors in the curve intensity are made for small total glucose values, which
are in the region where the initial rate fitting occurs. The
k1 values at 3 and 5% are equal within error, and the result of the initial-rate
approach at these two fractions (Table 1: k1 = 0.055 ± 0.003) agrees well within the SE with
k1 determined using the plasma-to-tissue glucose equilibrium ratio and
Eq.
11 (Table 1: 0.052 ± 0.001). It
should be noticed that this agreement is not due to the fact that the
plasma-to-tissue glucose equilibrium ratio is used to correct the
curves, because very different
k1 values are
found for the individual cats when the
k1 numbers
determined from
k2 + k3 and from the
initial rates at fvas = 3-5%
(e.g., cats
2 and
3) are compared. To see whether the
chosen plasma-to-tissue glucose ratio influences the agreement between
the initial rate and total-curve determination of
k1, we fitted our
results at two other
-to-
ratios for a vascular fraction of 5%. The results (Table
2) show that the average
k1 from both
approaches is again comparable.
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Table 1.
Plasma glucose concentrations (from glucose analyzer) and hyperglycemic
rate constants k2 + k3 and k1
determined from individual cat data for different vascular fractions
|
|
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Table 2.
Hyperglycemic rate constants obtained using different
CtotP, eq/CtotE, eq
ratios for curve correction at a 5% vascular fraction
|
|
Determination of unlabeled glucose levels in blood during the
infusion protocol.
To determine the plasma levels of nonenriched glucose during the
infusion protocol, we used blood samples of two cats to perform mass
spectroscopy. The results for both cats were similar, and Fig. 3 shows the data for one of these
cats, in which blood glucose levels were ramped up quickly to ~9 mM
and then more slowly increased to 16 mM (290 mg/dl). It is clear from
this figure that the unlabeled (12C) glucose level remains stable
within the error of the measurement, despite the hyperglycemic level of
the total blood glucose. The correspondence between the glucose
analyzer and the GC-MS data is good. It is interesting that the
analyzer generally gives a 10% higher value than GC-MS, but this will
not significantly influence the calculations performed in calibration
of the normalized experimental NMR curve.

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Fig. 3.
Comparison of GC-MS results with glucose analyzer data for arterial
blood glucose. Levels of labeled and unlabeled glucose measured by
GC-MS are indicated by and , respectively. Result clearly
indicates that unlabeled glucose level remains constant for duration of
experiment; and , total glucose measured by analyzer and GC-MS,
respectively, which are equivalent within error of measurement.
|
|
Extract studies.
Figure 4,
A and
B, shows extract spectra taken in vivo
and postmortem. The reliability of the in vivo study is confirmed by the low level of the
[1-13C]lactate
resonance at 21 ppm, which should not be confused with the acetate
standard. Lactate is very high in the postmortem spectrum. Figure 4,
C and
D, shows close-ups for the
[1-13C]glucose region,
which contains resonances for
- and
-isomers of
[1-13C]glucose (at
92.9 and 96.8 ppm, respectively) and
[1-13C]G-6-P
(at 93.11 and 96.95 ppm, respectively). It can be seen that the
contribution of
[1-13C]G-6-P
to total labeled glucose is negligible in both spectra, confirming the
validity of the simplified approach using three compartments. To
confirm the correctness of this result, we also prepared a phantom with
approximately equal amounts of
[1-13C]glucose and
[1-13C]G-6-P
(Fig. 4E). This spectrum shows that
the two resonances can indeed be separated. Finally, Fig.
4F shows the relevant glucose region
for a heart extract. In this organ the
[1-13C]G-6-P
concentration is higher than in the brain and can be clearly distinguished. However, on the basis of the relative integrals of the
two resonances, the use of negligible
[1-13C]G-6-P
should still be a good assumption to study glucose transport and
metabolism in the heart too.

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Fig. 4.
High-resolution 13C spectra
(13C frequency 125 MHz; 11.7 T
Magnet) of brain extracts collected in vivo
(A,
C) and postmortem
(B,
D). Spectra for a phantom with both
[1-13C]glucose
6-P and
[1-13C]glucose are
shown in E. Spectrum of a heart
extract (high-working heart preparation perfused with buffer containing
[1-13C]glucose,
[U-13C]palmitate,
ketone bodies, Krebs solution, blood, and insulin) is given in
F. Success of in vivo brain experiment
is confirmed by low lactate level (resonance at 21 ppm). Standard is 1 mM acetate (at 24 ppm). Sample sizes and number of scans were 200 mg/3
ml tissue (20,000 scans), 1.6 g/3 ml tissue (10,000 scans), ~1 mM
(6,000 scans), and 2 g/3 ml (8,000 scans) for in vivo brain, postmortem
brain, phantom, and heart, respectively. Data show negligible presence
of [1-13C]glucose
6-P (resonances at 96.95 and 93.11 ppm
for - and -isomers, respectively) in brain and only a small
contribution (<4%) in heart. GABA, -aminobutyric acid; glu,
glutamate; gln, glutamine.
|
|
 |
DISCUSSION |
The results in Table 1 show that dynamic
13C NMR spectroscopy can directly
provide the quantity
k2 + k3 and thus the
tissue glucose half-life time at hyperglycemia. It is important to
realize that this parameter is independent of
/
(Tables 1 and 2) and can be obtained from a simple exponential curve
fit of the normalized experimental signal intensities. Thus the
accuracy of this parameter depends only on the assumptions made in the
derivation of the rate equations and on the experimental accuracy of
the signal intensities. The quality of the NMR data (e.g., Fig. 2) and
the very small standard deviation of only 8% indeed indicate good
experimental accuracy, and the assumptions made in deriving the rate
equations have also been well tested. First of all, our experiments
(Fig. 2) show that plasma glucose is already constant at hyperglycemia
within 0.5 to 2 min, whereas the first spectrum (average over the first
84 s) shows only a small change with respect to control. Thus the
derivation based on a constant total blood glucose level during the
experiment is well founded. Second, our extract data show convincingly
that the concentration of phosphorylated glucose is negligible compared with total glucose, thereby validating the use of the simplified Eqs.
10-12
for total glucose. Third, the GC-MS data indicate that the unlabeled
glucose concentration is stable during the duration of our experiments
in the cat, supporting the initial assumptions in
Eqs.
1 and 2, in which the nonlabeled glucose
does not contribute to the change in total glucose. Fourth, the results
in Table 1 show that the determined hyperglycemic
k2 + k3 values are
independent of the vascular fraction and therefore can be determined
accurately from the experimental data without any assumptions. However,
to determine k1
it is necessary to assume a certain plasma-to-tissue glucose ratio,
whereas determination of CMRGlc
requires an additional assumption.

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Fig. 5.
Plots of Tmax
(A) and
CMRGlc
(B) at different
Kt values vs.
plasma-to-tissue glucose equilibrium ratio at normoglycemia
(CtotP, eq = 4.0 mM). Functions
describing relationships between these parameters are given in
Eqs.
17,
19, and
22, and parameters are derived from
experimentally determined
k2 + k3 value at
CtotP, eq = 24.9 mM.
|
|
The results in Tables 1 and 2 indicate that the
k1 values
determined by the initial rate approach at vascular fractions 3-5% are equal (within SD) to the ones obtained from
k2 + k3 and
/
using Eq.
11. This confirms the accuracy of our
model, especially the assumption of unidirectional metabolism. Because
the initial rate approach is less accurate than the use of
Eq.
11, we will use the
k1 values derived
from k2 + k3 in our
subsequent calculations. It is clear from Tables 1-3 and from
Eq.
11 that the choice of
/
will profoundly influence
k1. In addition,
further analysis of the results in terms of cerebral influx and
utilization rates and the comparison of these rates with the literature
are complicated by the fact that the rate constants
k1-k3
determined in dynamic uptake experiments are concentration dependent.
This dependence is expressed in the relationship between Sokoloff's
constants and the Michaelis-Menten parameters for the individual rate
constants k1
and
k2
|
(19)
|
in
which Tmax (in
µmol · g
1 · min
1) and
Kt (in mM) are the Michaelis-Menten maximum
glucose transport rate and half-saturation constant, respectively.
Notice that all concentrations are in millimolar units, which is
required based on Eq.
1, in which the use of equal units for
the rate constants (min
1)
corresponds to equal units for the concentrations. Combination of
Eqs.
17 and 19 gives
|
(20)
|
It
is important to see the implication of this equation, namely that the
Tmax-to-CMRGlc
ratio, Kt, or
the
CtotP, eq-to-CtotE, eq ratio is concentration dependent. It seems unlikely that glucose transport parameters will change in acute hyperglycemia, and it has
been documented that hexokinase is saturated
[K haset = 0.067 mM (Ref. 16)] at a very low tissue glucose concentration, leading to a concentration-independent
CMRGlc (10, 16, 20). Thus it has
to be concluded that the
CtotP, eq-to-CtotE, eq ratio depends on the plasma glucose concentration. To determine all
relevant parameters, we use the
CtotP, eq-to-CtotE, eq ratio at normoglycemia (CtotP, eq = 4 mM) and a Kt = 5 ± 1 mM to determine
Tmax,
CMRGlc and the normoglycemic CIRGlc from our experimentally
determined k2 + k3 value at
hyperglycemia. This can be achieved by calculating
Tmax/CMRGlc
from Eq.
20 at normoglycemia and using this
value to determine
CtotP, eq/CtotE, eq at hyperglycemia (CtotP, eq = 24.9 mM). From this number, Eq.
19 can be used to determine
Tmax and
Eq.
20 to subsequently determine
CMRGlc. The influence of
Kt and the
normoglycemic tissue-to-plasma glucose ratio on this determination is
depicted in Fig. 5, A
and B. Our numbers (Table
3) compare well with a recent
literature compilation of gray matter radiolabel data by Gjedde (9) as well as with a recent compilation of static
13C and dynamic proton NMR
transport studies from human NMR (12). To judge whether this is
reasonable, we obtained MR images to determine the gray-to-white matter
ratio in brain slice chosen for our cat studies. Figure
6 shows a coronal image with a typical slice position
indicated. Using a voxel count of the gray and white matter regions, we
determined that the gray-to-white matter ratio of the total area is
~80:20%. Because white matter has about one-half the aerobic
metabolic rate (9) of gray matter and because rates are expected to be
lower in anesthetized animals, it can be concluded that there is good
agreement between our metabolic and transport data in an area of
predominantly gray matter in the anesthetized cat with data from
literature on gray matter in the awake human. Actually, with the use of
our experimentally determined
k2 + k3 value and the
plausible Kt = 5 ± 1 mM, the range of possible
Tmax and
CMRGlc values is limited (Fig. 5
and Table 3), because a reasonable corresponding
CtotP, eq/CtotE, eq value has to exist (Eq.
20). With the use of our results,
some insight can be obtained into recent data obtained by Gruetter et
al. (12), who gave two potential combinations of
Kt,
Tmax, and
CMRGlc values, namely the ones in
Table 3 and another combination, Kt = 4.8 mM,
Tmax = 0.80 µmol · g
1 · min
1,
and CMRGlc = 0.32 µmol · g
1 · min
1.
However, this second series leads to a
CtotP, eq-to-CtotE, eq ratio of 14.4 and therefore can be discounted. We would also like to
point out that, based on Eq.
19,
Tmax can be
determined within a small range by measuring
CtotP, eq/CtotE, eq and k2 + k3 at
hyperglycemia because the contribution of
Kt is small in
the denominator. To obtain an experimental value for Kt for more
accurate determination of CMRGlc,
the rate constants have to be studied as a function of concentration.

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Fig. 6.
Spin-density/T2-weighted MRI image (repetition time = 3 s; echo time = 60 ms) of a 2-mm coronal slice showing the typical position of 8-mm
slice used in our glucose uptake studies. Cerebral spinal fluid is
bright, white matter is dark, and gray matter is gray.
|
|
In summary, we have designed a new glucose-uptake NMR spectroscopy
experiment to determine tissue glucose utilization half-life times from
a simple exponential fit of the experimental signal intensities. It was
demonstrated that this model simplification is allowed for the brain
through NMR extract studies, which showed a negligible concentration of
phosphorylated glucose compared with glucose. One organ that should
also be suitable for this approach is the heart, in which the
phosphorylated glucose concentration is <4% of the total glucose
concentration (Fig. 4F). The
validity of this simplification for other tissues needs to be
established using extract studies. The rate constants of brain glucose
influx and utilization determined using this new approach are in the same order of magnitude as those obtained from previous PET and NMR
studies, but the present approach is simpler. One important reason that
the rates can be determined accurately is because the rate constants
(not the rates) of transport and metabolism are slowed down at
hyperglycemia. Actually, the principles established in this paper can
also be applied to dynamic PET studies of radiolabeled [11C]- or
[14C]glucose. These
studies are normally complicated by the fact that labeled metabolic
products are impossible to distinguish from labeled glucose,
necessitating the use of glucose analogs such as fluorodeoxyglucose.
With the use of hyperglycemia (unlabeled glucose hyperglycemic steady
state), it should be possible to slow down glucose utilization so that
the glucose uptake curve reaches equilibrium before appreciable amounts
of the first metabolic product (glutamate) are formed. The use of
natural radioactively labeled glucose analogs and the possibility to
measure half-life times with a single exponential data fit should allow
accurate localized pathology studies using PET. Because PET studies use tracer concentrations, the labeled and unlabeled blood glucose concentrations can easily be kept stable and all rate equations derived
here apply. Similar arguments hold for proton NMR, but, although
metabolic products should be distinguishable, these measurements are
complicated by the fact that difference spectroscopy has to be
performed and that present sensitivity may be too low to perform time-resolved imaging studies. However, technical progress in NMR is
ever continuing, and it may be possible that some of these problems can
be solved in the near future.
 |
ACKNOWLEDGEMENTS |
We are grateful to Daryl DesPres for the animal preparations at the
National Institutes of Health (NIH) and to Drs. M. Miyabe and J. Ulatowski for help with some of the experiments at Johns Hopkins. We
also thank Dr. Richard Traystman for supporting this research, Drs.
Jianhui Shi and Jack Cohen for helpful discussions, Alan Olsen and Dr.
V. P. Chacko for technical support, and Drs. David Cohen and Maren
Laughlin for helpful comments with the manuscript.
 |
FOOTNOTES |
The heart extract data were obtained as part of an ongoing
collaboration (D. Davis) with Drs. John Forder and John Chatham. Part
of this work was performed in the NIH In Vivo NMR Research Center.
This research was supported by the Whitaker Foundation and NIH Grant
NS-31490.
Part of this work was done during the tenure of an established
investigatorship from the American Heart Association (S. Eleff and
P. C. M. van Zijl).
Preliminary accounts of this work were presented at the 11th Annual
Meeting of the Society of Magnetic Resonance in Medicine in Berlin
(1992; abstract p. 550), the Workshop on Advances in Physiological
Chemistry by In vivo NMR, Cape Cod, MA (1995), and at
the Joint Meeting of the Society of Magnetic Resonance and the
European Society for Magnetic Resonance in Medicine and
Biology in Nice, France (1995; abstract p. 271).
Address for reprint requests: P. C. M. van Zijl, Johns Hopkins Univ.
Medical School, Dept. of Radiology, 217 Traylor Bldg., 720 Rutland Ave,
Baltimore, MD 21205.
Received 25 March 1997; accepted in final form 22 August 1997.
 |
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