Determination of local brain glucose level with
[14C]methylglucose:
effects of glucose supply and demand
Gerald A.
Dienel1,
Nancy F.
Cruz1,
Keiji
Adachi1,
Louis
Sokoloff1, and
James E.
Holden2
1 Laboratory of Cerebral
Metabolism, National Institute of Mental Health, Bethesda, Maryland
20892; and 2 Department of Medical
Physics, University of Wisconsin Medical School, Madison, Wisconsin
53706
 |
ABSTRACT |
Methylglucose can be
used to assay brain glucose levels because the equilibrium
brain-to-plasma distribution ratio for methylglucose (C*e/C*p)
is quantitatively related to brain
(Ce) and plasma
(Cp) glucose contents. The
relationship between Ce and
C*e/C*p
predicted by Michaelis-Menten kinetics has been experimentally
confirmed when glucose utilization rate
(CMRGlc) is maintained at
normal, resting levels and Cp is
varied in conscious rats. Theoretically, however,
Ce and
C*e/C*p
should change when CMRGlc is
altered and Cp is held constant;
their relationship in such conditions was, therefore, examined
experimentally. Drugs were applied topically to brains of conscious
rats with fixed levels of Cp to
produce focal alterations in
CMRGlc, and
Ce and
C*e/C*p
were measured. Plots of Ce as a
function of
C*e/C*p
for each Cp produced straight lines; their slopes decreased as
Cp increased. The results confirm that a single theoretical framework describes the relationship between
Ce and
C*e/C*p
as either glucose supply or demand is altered over a wide range; they
also validate the use of methylglucose to estimate local
Ce under abnormal conditions.
cerebral glucose utilization; brain hexose transport
 |
INTRODUCTION |
MANY ABNORMAL and pathophysiological conditions alter
local rates of glucose utilization
(CMRGlc) in brain, which in turn cause the level of glucose in the tissue to vary. Metabolic mapping techniques are often used to detect and quantify abnormal brain function in affected structures, monitor the evolution of the condition, and evaluate the efficacy of treatment in experimental animals and human subjects. Determination of
CMRGlc, particularly under abnormal conditions, requires knowledge of the local tissue glucose content so that the appropriate value of the lumped constant is
used to calculate CMRGlc when
[14C]deoxyglucose
([14C]DG) or
2-[14F]fluoro-2-deoxy-D-glucose
is used as the tracer (3, 10, 11, 23, 24, 26, 28-30). The lumped
constant of the
[14C]DG method is
relatively stable in normoglycemia and hyperglycemia, but it rises
sharply when the brain glucose level drops below ~1 mmol/g (e.g., as
in Refs. 3, 6, 23, 24, 26, and 30). Also, when labeled glucose is used
as the tracer, local glucose levels must be determined so that the
proper value for the brain-to-plasma distribution ratio for glucose is
used to calculate CMRGlc in each
structure (13).
Radiolabeled
3-O-methyl-D-glucose
(methylglucose) can be used to assay local glucose levels in brain by
direct measurement or by quantitative autoradiography, because the
equilibrium brain (C*e)-to-plasma
(C*p) distribution ratio for
methylglucose
(C*e/C*p) varies quantitatively with brain
(Ce) and plasma
(Cp) glucose contents (1, 10).
The methylglucose distribution ratio is used to determine the local
glucose content in brain, which in turn specifies the appropriate value
for the lumped constant (10, 11). When the relationship
between
C*e/C*p
and Ce was experimentally determined by changing Cp to alter
Ce (i.e., control of
Ce mainly by delivery),
C*e/C*p
progressively increased as Cp
and Ce were reduced from
hyperglycemic to hypoglycemic levels, in good agreement with
results predicted by Michaelis-Menten kinetics for glucose and methylglucose transport across the blood-brain barrier (1, 6, 10,
11, 14). Thus these studies tested and validated the use of
Eq. A2 (see
APPENDIX for equations throughout
paper) to estimate Ce from
measured values of Cp and
C*e/C*p
when metabolic demand for glucose in brain was normal.
Theoretical considerations predict, however, that if metabolic demand
were increased and Cp were kept
constant,
C*e/C*p
would fall rather than increase with decreasing
Ce (11, 14); conversely, C*e/C*p
should increase with increasing Ce
as metabolic demand decreases (see Eq. A1). Our preliminary experiments confirmed these predictions and demonstrated that, when
Cp was constant and in the
normoglycemic range,
C*e/C*p
decreased rather than increased when
Ce fell because of stimulation of
CMRGlc (8, 20). Thus measured
values for
C*e/C*p
and Ce determined when glucose
delivery is the predominant factor controlling brain glucose levels (6, 11) would not be expected to be appropriate for determination of local
glucose levels under conditions in which
CMRGlc is abnormal.
Because their values cannot be directly measured in all possible
conditions, brain glucose levels must be computed from measured values
for Cp and
C*e/C*p,
with presumed values for the half-saturation concentration for the
transport of glucose
(Kt) and the
maximal distribution space for hexose in tissue relative to that in
plasma (S), i.e., relative brain
water content. The accuracy of calculated Ce depends, in part, on the
assumption that Cp and
C*p, measured in blood drawn from a
peripheral artery, closely approximate the concentrations of these
hexoses in brain capillaries, which cannot be directly measured. The
objective of the present study was to determine whether measured and
model-predicted glucose levels are equivalent when both glucose supply
and glucose demand are varied over a wide range.
CMRGlc was, therefore, altered in
brains of conscious rats with constant plasma glucose levels (within the range of ~4-18 mM) by sustained drug-induced focal
convulsive activity and focal depression of metabolism. The results of
the present study demonstrate good agreement between measured and calculated values for Ce and
C*e/C*p
and confirm that relationships among
Ce,
Cp, and
C*e/C*p
predicted by Eq. A2 remain valid when tissue glucose content is altered over a wide range by changes in
either glucose supply or demand. The results also identify conditions
in which accurate estimates of tissue glucose level might not be
obtained with the methylglucose method.
 |
MATERIALS AND METHODS |
Theory and experimental design.
Equations describing the relationships among
Ce,
Cp, and
C*e/C*p,
with Kt and
S as parameters, are derived in the
APPENDIX.
Previous work (6, 10, 11, 14) tested the relationships among
Ce,
Cp, and
C*e/C*p
in the case of fixed demand and variable supply (Eqs.
A10 and A11). The
current experiments were designed to test these relationships in the
alternative case of varying demand and fixed supply
(Eqs. A1 and A2) by varying
CMRGlc while Cp was maintained at different but
constant levels within the range of 4-18 mM. Local
CMRGlc rates in cerebral cortex of
conscious rats were changed by topical application of drugs to the dura via four burr holes through the skull to produce simultaneously increases and decreases in CMRGlc
in different regions of cerebral cortex and thus cause secondary
changes in Ce in the drug-treated tissue regions. Then tracer amounts of
[14C]methylglucose
were infused intravenously for ~60 min to achieve a steady state, the
brains were frozen in situ, and drug-treated tissue samples were
dissected out and assayed for their hexose contents; untreated samples
of cerebral cortex from the same brains were also dissected out to
obtain tissue with normal or near-normal CMRGlc and little, if any, change
in Ce. Thus many pairs of
Ce and
C*e/C*p
were measured in extracts of dissected tissue samples exposed to the
same Cp, all obtained from the
same brain. The experimentally determined relationships between
Ce,
Cp, and
C*e/C*p were analyzed by model-dependent fitting routines, and a contour map
was constructed so that Ce could
be obtained from measured values of
Cp and
C*e/C*p.
The combined results of the present and previous studies were used to
establish and validate a contour map to determine
Ce from the relationship between
measured values for
C*e/C*p
and Cp that can be applied to
assays of local glucose levels when either or both supply and demand
are altered.
Surgical procedures.
Normal male Sprague-Dawley rats weighing 300-450 g were obtained
from Taconic Farms (Germantown, NY) and were fed rat chow ad libitum
until the day before the experiment. Fed rats were used to obtain
higher steady-state levels of glucose in plasma, whereas other groups
were fasted overnight to reduce their plasma glucose levels. On the day
of the experiment the rats were anesthetized with halothane
(1-1.5%, maintenance dose) in 70%
N2O-30%
O2, and catheters were inserted
into a femoral artery and vein. Four burr holes ~2 mm in diameter and
placed ~2.5 mm lateral to the sagittal suture and ~2 mm caudal or
rostral to bregma were drilled through the skull with a trephine; the
drill was periodically cooled in ice-cold saline to minimize heating
that could damage underlying tissue, and care was taken not to cut or
damage the dura. The burr holes were covered with Gelfoam (Upjohn,
Kalamazoo, MI) soaked in 0.9% saline, the rats were restrained with a
loose-fitting plaster cast around the lower torso, and
2.5 h were
allowed for recovery from surgery before the experimental procedure.
Rectal temperature was monitored with a thermistor (Yellow Springs
Instrument, Yellow Springs, OH) and maintained at 37°C with a
thermostatically controlled heating lamp. Arterial blood
PO2,
PCO2, and
pH were determined with a model 170 pH-blood gas analyzer (Corning
Medical Scientific, Medfield, MA). Arterial blood hematocrit was
determined from blood samples after centrifugation. Mean arterial blood
pressure was measured with an air-damped Hg manometer. Arterial plasma glucose levels were assayed with a Glucose Analyzer 2 (Beckman Instruments, Fullerton, CA).
All animal use procedures were in strict accordance with the National
Research Council Guide for the Care and Use of
Laboratory Animals and were approved by the local
animal care committee.
Experimental procedures.
Fed and fasted rats were used to obtain arterial plasma glucose levels
in the mild hyperglycemic range (i.e., 13-18 mM) and normoglycemic
range (i.e., 8-10 mM), respectively. Insulin (Regular Iletin I;
Eli Lilly, Indianapolis, IN; 0.25-0.5 U/kg iv) was given to fasted
rats to further depress their plasma glucose concentration to levels in
the lower normoglycemic range (i.e., 6.5-7.4 mM) and the
mild-to-moderate hypoglycemic range (i.e., 4.3-5.7 mM). Plasma
glucose levels were monitored at 5- to 10-min intervals to establish
the baseline value for each animal, to track changes after insulin
injection, and to verify constancy throughout the experimental
interval. About 30 min after the plasma glucose concentration had been
maintained at a stable level, bicuculline methiodide (Sigma Chemical,
St. Louis, MO; 2 or 10 mM freshly prepared stock solution in 0.9% NaCl
containing 10 mM sodium phosphate, pH 7.2-7.4; total dose, 8 or 40 nmol to produce focal seizures) and muscimol (Sigma Chemical; 20 mM
freshly prepared stock solution dissolved in 0.9% NaCl containing 10 mM sodium phosphate, pH 7.2-7.4; total dose, 20 or 80 nmol to
produce focal depression of metabolism) were topically applied to the
surface of the intact dura. The bicuculline and muscimol were applied
either once (lower doses) or four times (1/4 of total dose per
application) at intervals throughout the experimental period. The first
dose of each drug was applied 20-30 min before the intravenous
injection of [14C]DG
or [14C]methylglucose;
subsequent applications were given immediately before injection of the
tracer and at ~20-min intervals thereafter, depending on the dose
schedule for each drug at each burr hole. Plasma glucose levels usually
remained constant if the animals were handled gently, particularly
during application of drugs, and if a quiet laboratory environment was
maintained; rats were not included in the study if their arterial
plasma glucose or [14C]methylglucose
levels deviated by more than ±10% during the experimental period.
The possibility of damage to the blood-brain barrier in the proximity
of the burr hole because of high local levels of bicuculline and
muscimol was examined in preliminary experiments. Rats were injected
intravenously with Evans blue dye [1 ml of 2% (wt/vol) dissolved
in 0.9% NaCl] 10 min before application of the drugs and were
killed 15-60 min later; there was no visible penetration of Evans
blue dye into the tissue under the burr holes (results not shown),
indicating that these drug treatments did not cause gross damage to the
blood-brain barrier.
Determination of CMRGlc and
[14C]methylglucose distribution
ratio.
Radiochemical purities of
2-deoxy-D-[1-14C]glucose
(51 mCi/mmol, Du Pont-NEN, Boston, MA) and
3-O-[methyl-14C]methyl-D-glucose
(57 mCi/mmol, Du Pont-NEN) were assayed before use by thin-layer
chromatography and/or by high-performance liquid chromatography, as previously described (6, 7), and found to be
>98%. Initial studies established the magnitude of focal activation
or depression of metabolism required to produce changes in the
[14C]methylglucose
distribution ratio. CMRGlc was
determined with the routine
[14C]DG procedure by
use of a 45-min experimental period (29). Briefly, timed samples of
arterial blood were drawn at frequent intervals after a pulse of 125 µCi/kg [14C]DG for
determination of plasma
[14C]DG and glucose
contents; levels of 14C in plasma
were assayed by liquid scintillation counting (Beckman model LS5801)
with external standardization. About 45 min after the pulse of tracer,
the rats were given a lethal dose of pentobarbital sodium and their
brains were rapidly removed, frozen in isopentane chilled to
40
to
50°C with dry ice, and stored at
80°C. Each brain was then cut into 20-µm-thick sections in a cryostat at about
20°C, dried at 60°C on a hot plate, and exposed to SB-5 X-ray film (Kodak, Rochester, NY). Local tissue concentrations of total
14C were determined by
autoradiography, and CMRGlc was
calculated with the operational equation of the method, with a value of
0.48 for the lumped constant (29).
Steady-state
C*e/C*p
values were determined by quantitative autoradiography in separate
groups of rats.
[14C]Methylglucose
(50-70 µCi/kg) was infused intravenously according to a program
designed to maintain a constant concentration of 14C in arterial plasma throughout
the experimental period (6); arterial blood was drawn at 5- to 10-min
intervals to monitor plasma glucose and
14C levels. Sixty minutes after
initiation of the infusion, a sample of arterial blood was drawn and
the rats were given a lethal dose of pentobarbital; their brains were
rapidly removed and processed for autoradiography, as described above.
The steady-state
C*e/C*p was calculated by dividing the brain
14C level by that in the last
plasma sample.
To determine relationships among
Cp,
Ce, and
C*e/C*p,
brain glucose levels and
C*e/C*p
values for
[14C]methylglucose
were determined in parallel in the same tissue samples by direct
chemical measurement. About 60 min after initiation of the programmed
infusion of
[14C]methylglucose,
rats were anesthetized rapidly with intravenous thiopental (25 mg/kg),
and their brains were immediately funnel-frozen in situ with liquid
nitrogen (25). When frozen, the heads were removed and transferred to
liquid nitrogen and stored at
80°C. Oxygen (100%) was
provided during the funnel-freezing procedure via a nose cone to
minimize tissue hypoxia. Immediately before and ~1 min after the the
start of the freezing procedure, additional samples of arterial blood
were taken for determination of the glucose and
14C contents of plasma; the mean
of these two samples was used for the plasma glucose level and to
calculate the
C*e/C*p.
Also, a second arterial blood sample was taken at 1 min
after the start of funnel-freezing for determination of
blood pH and gases.
Sampling, extraction, and analysis of brain tissue.
Frozen heads from 21 rats were warmed to about
25°C in a
cryostat; skin, muscle, and skull were removed; and superficial membranes and blood vessels were carefully scraped from the surface of
the cerebral cortex. Samples of frozen cerebral cortex (5-12 from
each brain) weighing ~5-15 mg were dissected out from cortex directly under the burr holes and from untreated cortical tissue located at various distances from the burr holes, weighed (at
25°C), and stored at
80°C until extracted with
aqueous ethanol as previously described (7). Each of the extracts was
stored at
80°C until it was analyzed for its
[14C]methylglucose
level by liquid scintillation counting and for glucose content by the
standard fluorometric enzymatic assay with hexokinase and
glucose-6-phosphate dehydrogenase (18). The measured concentrations of
glucose and
[14C]methylglucose in
each of the samples derived from each brain were then corrected for
corresponding hexose contents of residual blood [this value was
assumed to be 2.6% (31) because of the presence of both large vessels
and capillaries in the dissected samples] in brain, and
C*e/C*p
values were calculated from the corrected brain concentrations of
glucose and
[14C]methylglucose and
the respective arterial plasma values (i.e., means of samples drawn
immediately before freezing and 1 min after initiation of
funnel-freezing). To summarize, a pair of measured values for glucose
and [14C]methylglucose
was obtained from each of the drug-treated (i.e., those with altered
CMRGlc) or untreated (i.e.,
control) tissue samples dissected out of each brain; thus many pairs of
tissue samples were assayed after exposure to the same measured plasma glucose level in each rat.
 |
RESULTS |
Physiological variables.
Topical application of bicuculline and muscimol did not cause
appreciable changes in physiological variables, and values of all
variables were similar in each of the experimental groups (Table
1).
Determination of drug dosages to alter
CMRGlc.
Experimental conditions for control of brain glucose concentration
mainly by substrate demand were first established in preliminary experiments by topical application of various doses of different drugs
(results not shown). We previously used penicillin and barbital to
produce focal changes in rates of glucose utilization in cerebral cortex and tissue glucose content, but we found that penicillin produced only small reductions in glucose level and that barbital sometimes caused vascular damage (20). Bicuculline and muscimol, therefore, were tested for their ability to alter
CMRGlc and found to be appropriate
for use in the present study; two doses of each drug were used to
produce a range of focal increases (up to ~2.5-fold) and decreases
(20-50%), respectively, in
CMRGlc in the cerebral cortex of
each rat (Table 2). Values of
C*e/C*p
were highest when CMRGlc was
normal (i.e., in untreated tissue) or lowered (i.e., in
muscimol-treated tissue), and
C*e/C*p
and Ce fell as CMRGlc rose (i.e., in
bicuculline-treated tissue) (Table 2). Because the normal value of the
lumped constant of the
[14C]DG method (i.e.,
0.48) was used, calculated CMRGlc
for some samples of bicuculline-treated tissue shown in Table 2 were
probably somewhat overestimated. Any such errors would, however, be
expected to be <30%, because the brain glucose content exceeded 0.8 µmol/g in almost all samples obtained from normoglycemic rats with
Cp ~10 mM. (Compare values in
Table 2 with those in Fig. 1 and Table 1 of Ref. 6).
C*e/C*p
did not change in the muscimol-treated samples shown in Table 2,
indicating that Ce can be
relatively stable even with a large (i.e., ~35%) decrease in
CMRGlc for 60 min;
C*e/C*p
did, however, rise above normal in muscimol-treated samples from the
other animals that were used to obtain the data shown in Figs.
1, 3, and 4. Thus topical application of
different doses of drugs through the burr holes provides the means to
produce focal variations in CMRGlc
in the brain of each conscious rat over approximately a threefold
range, broad enough to obtain 5-12 pairs of values from tissue
with normal and altered CMRGlc for Ce and
C*e/C*p
for the same Cp in one rat.
View this table:
[in this window]
[in a new window]
|
Table 2.
Influence of bicuculline and muscimol on rate of glucose utilization
and brain-to-plasma distribution ratio for methylglucose
|
|

View larger version (20K):
[in this window]
[in a new window]
|
Fig. 1.
Influence of glucose demand on relationship between brain glucose level
and steady-state brain-to-plasma distribution ratio for
[14C]methylglucose.
Solid and dotted contour lines are theoretical relationships predicted
by Eqs. A2 and A8.
Vm/Vt,
ratio of Michaelis-Menten kinetic constants for maximal velocity of
phosphorylation of glucose by hexokinase to that of transport of
glucose across the blood-brain barrier. Solid lines, conditions of
fixed supply of glucose as demand is varied; dotted lines, conditions
of fixed demand for glucose (expressed in our theoretical model as
Vm/Vt)
as supply is varied. Data points, measured pairs of values for brain
glucose content (Ce) and
brain-to-plasma distribution ratio for
[14C]methylglucose
(C*e/C*p)
assayed in individual tissue samples from the funnel-frozen brains of 4 representative rats, each with a different plasma glucose level. Local
rates of glucose utilization in cerebral cortex were altered by topical
application of bicuculline and muscimol while plasma glucose
concentration (Cp) was
maintained at level shown throughout experiment. Data points are thus
aligned along solid lines. Under these conditions of fixed supply and
variable demand, relationship between
Ce and
C*e/C*p
has a positive slope, and the slope value increases as the level of
Cp increases. The 4 animals were
selected from the total of 21 studied, with fixed
Cp values ranging from 4 to 18 mM.
|
|
Influence of CMRGlc and
Cp on the relationship between
Ce and
C*e/C*p.
Representative results from both the current and previous experiments
are presented as data points on plots of
Ce vs.
C*e/C*p in Figs. 1 and 2. These figures also
include solid and dotted contour lines calculated according to the
theory developed in the APPENDIX. The
solid lines show predicted relationships of
Ce vs.
C*e/C*p
calculated by Eq. A2; there is a
different line for each Cp value
(see DISCUSSION). The dotted lines
were calculated according to Eq. A8
and show lines for different values of the metabolic demand parameter
R = Vm/Vt,
where Vm and
Vt are the Michaelis-Menten maximal velocity constants for
phosphorylation and blood-brain barrier transport of glucose,
respectively (see APPENDIX and
DISCUSSION). The
Vm/Vt
rises above the normal value of ~0.32 (1, 14) (also see Fig. 2) when
the maximal rate of glucose phosphorylation by hexokinase increases
relative to that of glucose transport across the blood-brain barrier
(e.g., during seizures when tissue glucose levels tend to fall), and it
falls below that value when glucose metabolism is reduced relative to
its maximal rate of transport (e.g., during coma or anesthesia when
tissue glucose levels tend to rise).

View larger version (26K):
[in this window]
[in a new window]
|
Fig. 2.
Influence of glucose supply on relationship between brain glucose level
and steady-state brain-to-plasma distribution ratio for
[14C]methylglucose.
Solid lines, theoretical relationships in conditions of fixed supply of
glucose; dotted lines, those in conditions of fixed demand (see Fig.
1). Two sets of data points correspond to conditions of fixed demand as
Cp (supply) is varied. Thus
relationships between the measured
Ce and
C*e/C*p
values are oriented along dotted lines. Relationship has a negative
slope; the magnitude of the slope decreases as demand increases. ,
Values from 49 individual animals obtained in our previous study (6,
14) in normal, conscious rats.
[14C]Methylglucose was
infused for 60 min while Cp was
clamped at values ranging from 4 to 28 mM. , Means of groups of rats
that were lightly sedated with pentobarbital sodium (15 mg/kg),
injected iv with
[14C]methylglucose,
and brains sampled 10 min later by funnel-freezing (11). Points from
normal, conscious rats (rate of glucose utilization is ~0.7
µmol · g 1 · min 1)
fall on a contour corresponding to a
Vm/Vt
approximately equal to 0.32; for those from sedated rats, the apparent
contour corresponds to a
Vm/Vt
approximately equal to 0.22.
|
|
When CMRGlc is varied while
Cp is fixed at a constant level,
Ce and
C*e/C*p
are predicted to change in the same direction, i.e., they increase and
decrease in parallel in a
Cp-dependent manner (Figs. 1 and
2, solid lines). Focal changes in
CMRGlc were experimentally induced
in brains of 21 rats with constant but different
Cp levels ranging from ~4 to 18 mM, and glucose content and
C*e/C*p
were determined in each of the 5-12 samples of tissue dissected
out of each brain. For clarity, pairs of measured glucose levels and
[14C]methylglucose
C*e/C*p,
determined in each tissue sample dissected from brains of only four
representative rats with different plasma glucose levels, are plotted
in Fig. 1. The values for each of these animals fell along or parallel
to the solid theoretical lines corresponding to the measured
Cp for that animal (i.e., 18, 9.6, 6.8, and 5.5 mM). For example, the two bicuculline-treated tissue
samples (i.e., those with focal seizures) dissected out of the
moderately hyperglycemic rat with
Cp = 18 mM had the lowest values
for glucose (<2 µmol/g, Fig. 1; for clarity, drug-treated samples
are not identified in the figure) and
C*e/C*p
(0.3-0.33) compared with all other samples obtained from that
animal; these two glucose-methylglucose pairs fell on the dotted line
corresponding to a higher-than-normal
Vm/Vt,
i.e., ~0.52 (Fig. 1, triangles). Untreated and muscimol-treated
samples dissected out of the same brain had higher glucose levels and
C*e/C*p
that corresponded to normal or subnormal values for
Vm/Vt;
the highest brain glucose levels in this brain exceeded 4.5 µmol/g
and corresponded to a below-normal
Vm/Vt,
i.e., ~0.23 (Fig. 1, triangles). Similar results were obtained in the
three other normoglycemic and moderately hypoglycemic animals (Fig. 1),
as well as in the other 17 animals assayed in the present study (data
not shown). The slope of the relationship between glucose content and
methylglucose distribution volume progressively decreased as the level
of Cp fell (Fig. 1), as predicted
by Eq. A2.
When Cp is varied while metabolic
demand is fixed at a constant value,
Ce and
C*e/C*p
values are predicted to change in opposite directions; the value for
one variable increases as that for the other decreases, and vice versa
(Figs. 1 and 2, dotted lines). Measured values obtained in our previous
study (6, 14) from 49 normal conscious rats, which had their plasma
glucose levels clamped at different levels to change
Ce mainly by supply, are plotted
in Fig. 2 (squares). When Cp
concentrations were clamped at increasingly higher levels within the
range of 4 to 26 mM, the measured level of glucose in brain of each
animal progressively increased, whereas the
C*e/C*p
values measured in the same samples became smaller; all measured points
fell along a line corresponding to a
Vm/Vt
of ~0.32 (Fig. 2, squares). On the other hand, measured values
obtained by Gjedde and Diemer (11) from rats given barbiturate (and
therefore expected to have a lower metabolic demand) fell along a line
corresponding to a lower
Vm/Vt,
i.e., ~0.22 (Fig. 2, triangles). Thus the highest values for
glucose-methylglucose distribution ratio pairs were associated with
lowest values for Vm/Vt;
conversely, the lowest levels for these pairs corresponded to higher
Vm/Vt
values (Figs. 1 and 2).
When measured and calculated values obtained in all samples from all
experimental animals were compared, good agreement was found for
Ce (Fig.
3; predicted results were calculated with
Eq. A2) and
C*e/C*p
(Fig. 4; predicted results were calculated
with Eq. A1). There was somewhat
more scatter about the line of identity for the 167 samples from 21 rats in which focal changes in metabolic rates were induced compared
with the 49 rats in which plasma glucose was clamped at different
levels [Figs. 3 and 4; compare filled ("Vary
CMRGlc...") to open ("Vary
Cp...") symbols in each
figure]. Also, estimates of
C*e/C*p
calculated from measured Ce and
Cp values (Fig. 4) appear to be
somewhat less variable than model-predicted glucose concentrations
calculated from measured
C*e/C*p
(Fig. 3 and see DISCUSSION).

View larger version (19K):
[in this window]
[in a new window]
|
Fig. 3.
Comparison of measured and model-predicted glucose levels in brain.
Ce levels were calculated with
Eq. A2 by use of
C*e/C*p
and Cp measured in present study
and values for half-saturation constant for glucose transport
(Kt, 6.56 mM) and
for physical distribution space for hexose in tissue
(S, 0.89 ml/g) determined from our
previous work (6, 14; also see Fig. 5).
CMRGlc, glucose utilization rate.
Solid line, line of identity. Regression line (not shown) calculated
for values obtained when control of brain glucose level is mainly by
demand ( ) is y = 0.71x + 0.76 (r = 0.77, P < 0.001, n = 167 from 21 rats); SE values of
slope and intercept are 0.05 and 0.10, respectively. Regression line
calculated for values obtained when control of brain glucose level is
mainly by supply ( ) is y = 1.02x + 0.11 (r = 0.99, P < 0.001, n = 49 rats); SE values of
slope and intercept are 0.02 and 0.06, respectively.
|
|

View larger version (18K):
[in this window]
[in a new window]
|
Fig. 4.
Comparison of measured and model-predicted methylglucose distribution
ratios. Methylglucose distribution ratios were calculated with
Eq. A1 by use of
Ce and
Cp measured in the present study
and values for Kt
(6.56 mM) and for S (0.89 ml/g)
determined from our previous work (6, 14; also see Fig. 5). Solid line,
line of identity. Regression line (not shown) calculated with values
obtained when control of
Ce is mainly by demand ( ) is
y = 1.02x 0.02 (r = 0.83, P < 0.001, n = 167); SE values of slope and
intercept are 0.05 and 0.03, respectively. Regression line calculated
with values obtained when control of
Ce is mainly by supply ( ) is
y = 0.95x + 0.02 (r = 0.98, P < 0.001, n = 49); SE values of slope and
intercept are 0.03 and 0.02, respectively.
|
|
 |
DISCUSSION |
Influence of glucose supply and demand on relationship between
glucose level and
C*e/C*p:
theory.
The combined results of our present and previous (6, 14, 20) studies
extend the elegant pioneering work of Buschiazzo et al. (1) and Gjedde
(10) and Gjedde and Diemer (11) to establish quantitative relationships
between the steady-state C*e/C*p
and Cp and
Ce levels under various
experimental conditions. The experimental results shown in Figs. 1 and
2 confirm predictions that, when
CMRGlc is relatively constant,
Ce and
C*e/C*p
change in opposite directions as
Ce is varied by clamping
Cp at different levels. In
contrast, when Ce is altered
mainly by variations in CMRGlc,
C*e/C*p
changes in the same direction as
Ce, with a different slope for
each value of Cp. Thus a single
theoretical framework derived from Michaelis-Menten competitive
kinetics for hexose transport across the blood-brain barrier (see
APPENDIX) provides reliable
estimates of steady-state brain tissue glucose levels over a wide range
of changes in glucose supply and/or demand. Either
Eq. A2 or a contour map can be used to
determine local glucose concentrations in brain under many, but not
all, possible conditions.
The lines in the contour map shown in Fig.
5 were calculated according to the theory
developed in the APPENDIX and
illustrate the interrelationships between
Ce and
C*e/C*p
at different values for Cp. The
solid lines were calculated by Eq. A2;
twelve different lines are shown for
Cp values, ranging from a minimum
of 4 mM (line at far right) in 2-mM steps to a maximum of 26 mM (line at far left). The dotted lines were calculated according to
Eq. A8; eight lines are shown, with
the metabolic demand parameter R = Vm/Vt
ranging from a minimum value of 0.10 (line at far right) in steps of
0.06 to a maximum value of 0.52. To calculate these contour lines
(Figs. 1, 2, and 5), the values used for
Kt (6.56 mM) and
for S (0.89 ml/g) were determined in
the present study by substitution of 49 triplets of measured values
(Cp,
Ce,
C*e/C*p) from our previous work (6, 14) into Eq. A1, followed by evaluation of
Kt and
S by least squares optimization. The
value for S represents the physical
distribution space for glucose and methylglucose in brain, i.e., the
water content of brain relative to that in plasma (14); thus the value
for S is slightly larger than the actual tissue water content used in previous studies (3, 10, 24). The
value for the half-maximal saturation constant for phosphorylation
(Km, 0.063 mM),
also derived from our measured data, was from our previous report (14).
As described in the APPENDIX, the
straight-line segments of the dotted lines that appear to crosshatch
with the solid curves are well approximated by Eq. A11.

View larger version (28K):
[in this window]
[in a new window]
|
Fig. 5.
Contour map to determine Ce when
either or both glucose supply and demand are varied. Solid contour
lines, relationship between Ce and
methylglucose distribution ratio when
Cp is held constant at values
shown (4-26 mM in 2-mM increments). Dotted lines, relationship
when
Vm/Vt
is held constant at values shown (0.10 to 0.52 in increments of 0.06).
Solid and dotted lines were calculated with Eqs.
A2 and A8,
respectively. Two of 3 model parameters
(Kt: 6.56 mM;
S: 0.89 ml/g) were determined by
substitution of 49 triplets of measured values
(Cp,
Ce,
C*e/C*p)
from our previous work (6, 14) into Eq. A1, followed by evaluation of
Kt and
S by least squares optimization. The
3rd parameter [half-maximal saturation constant for
phosphorylation
(Km), 0.063 mM], also derived from our data, was taken from our previous
report (14). As described in APPENDIX,
straight-line segments of dotted curves are well approximated by
Eq. A11.
|
|
When CMRGlc is varied while
Cp is fixed at a constant level,
Ce and
C*e/C*p
are predicted to change in the same direction, i.e., they increase and
decrease in parallel (Fig. 5, solid lines). For example, when
Cp = 8 mM and demand for glucose
is increased relative to the rate of glucose supply (i.e.,
Vm/Vt
rises from 0.1 to 0.52), Ce is
predicted to fall from ~4.8 to 0.5 µmol/g, causing the theoretical
C*e/C*p
to decrease from ~0.73 to 0.43 ml/g (Fig. 5). Also, when
Cp is clamped at progressively
lower levels from 26 to 4 mM, the slopes of the solid lines are
predicted to decrease, indicating that
C*e/C*p
is most sensitive to changes in Ce
when Cp is lowest (Fig. 5, solid
lines).
When Cp is varied while metabolic
demand is fixed at a constant value,
Ce and
C*e/C*p
are predicted to change in opposite directions; the value for one
variable increases as that for the other decreases, and vice versa
(Fig. 5, dotted lines). For example, when
Vm/Vt
is fixed at 0.34 and Cp is clamped
at progressively decreasing levels from 26 to 4 mM,
Ce should decrease from ~5 to
0.5 µmol/g, causing the theoretical
C*e/C*p
to rise from ~0.33 to 0.6 ml/g (Fig. 5). Also, when metabolic demand
rises relative to supply (i.e., when
Vm/Vt
increases from 0.10 to 0.52), the slope of each dotted line is
predicted to decrease progressively, indicating that
C*e/C*p
is most sensitive to changes in tissue glucose concentration when
consumption of glucose is highest relative to its rate of influx into
brain (Fig. 5, dotted lines).
In summary, changes in the equilibrium
C*e/C*p
as a function of Ce level are
greatest when metabolic demand for glucose is highest and
Cp levels are lowest. This
sensitivity of
C*e/C*p to tissue glucose level is apparent in Fig. 5 when it is viewed by
rotation of the figure 90° counterclockwise so that glucose level
is the abscissa and
C*e/C*p
is the ordinate. The method is most sensitive to changes in glucose
level that would have the highest impact on calculated
CMRGlc values.
Application of
C*e/C*p
to determine glucose level.
Use of methylglucose to estimate glucose level in brain tissue in vivo
(1, 6, 10, 11, 14, 20) or to evaluate hexose flux to and from tissue or
distribution kinetics and volume in vitro (21) or in vivo (22, 32) does
not depend on identity of the theoretical model and the biological
system with many cellular compartments; the simplest model that
provides accurate predicted values is most appropriate. In the present
study, the transport-based model can be applied to a wide range of
conditions; predicted glucose levels were, however, sometimes negative,
i.e., when measured Ce values were
very low (Fig. 3). Discrepant results could arise for various reasons:
increased hexose extraction fraction, inaccuracies in estimates of the
true values of S (relative brain water
content) or Kt,
changes in S or
Kt under the
experimental condition, and differences in the distribution of
methylglucose and glucose into various brain compartments.
Use of the methylglucose method is appropriate when the concentrations
of glucose and methylglucose in blood samples drawn from a large artery
approximate those in brain capillaries. Because the experimental
results obtained in the present study are in good agreement with most
of the theoretically predicted values (Figs. 1-4), this assumption
appears to hold under nearly all experimental conditions employed in
this study for the Cp range of
5.5-18 mM. Accurate estimates for
Ce should also be obtained when
plasma glucose exceeds 18 mM, because the hexose extraction fractions would be expected to decrease as plasma glucose levels rise, and the
arterial and capillary hexose levels would be essentially the same. On
the other hand, when CMRGlc
exceeds the rate of glucose supply to the brain in hypoglycemic
animals, the extraction fraction for glucose would increase, causing overestimation of the true capillary level and errors in calculated
Ce.
The brain compartments into which glucose and
[14C]methylglucose
might distribute (e.g., extracellular fluid spaces, different cell
types, and various intracellular spaces) appear to be "kinetically invisible" over nearly the entire range of glucose levels
investigated in the present study. The experimental data obtained in
normal, conscious rats fall along a line corresponding to a theoretical Vm/Vt
approximately equal to 0.32 (Fig. 2; also see Refs. 1 and 14),
supporting the assumption that transport is not rate limiting for
glucose utilization and that intracellular concentrations of glucose
and methylglucose can be maintained at levels close to those in the
extracellular fluid over a wide supply-demand range (14, 19, 27).
Regardless of site(s) of the rate-limiting step(s) that ultimately
control brain tissue and plasma hexose levels, the theoretical model
accurately takes into account effects of well-established differences
in Cp and
Ce (1, 3, 6, 11, 19, 20, 23, 24,
27). However, at very low glucose levels, intracellular glucose would
approach zero faster than the extracellular glucose level, and
compartmentation might contribute to errors in model-predicted glucose
concentrations.
Values for S [i.e., 0.7-0.8
(1, 11, 14)] and
Kt [i.e.,
6-14 mM (1, 4, 11, 14, 19, 23, 24)] have been determined in
different laboratories by direct measurement and/or by
model-dependent fitting of experimental results. Good agreement between
measured and theoretical results in the present study indicates that
values for S and
Kt, derived from
the data sets in our present and previous studies (6, 14) and used to
calculate the predicted values, were sufficiently close to the true
values and that they could be used to accurately estimate
Ce levels. Because calculation of
Ce with Eq. A2 includes the factor
(Kt + Cp), the calculated value of
Ce from measured values of
Cp and C*e/C*p
is expected to be least sensitive to inaccurate estimates of
S or
Kt when
Cp is high. Thus, as
Cp increases, the sum
(Kt + Cp) would progressively diminish
the fractional effect of errors in the estimate of the true value of
Kt on calculated
Ce; the magnitude of error would
be expected to increase as Cp
decreases.
Similar Cp-dependent sensitivity
to errors in calculated Ce would
be expected with any unknown changes in the values of
S or
Kt under abnormal
or pathophysiological conditions. For example, pentobarbital treatment
decreases Kt and
Vt of the
blood-brain barrier transporter for glucose (12, 15) and methylglucose (22), probably by direct interaction with the GLUT-1 transporter in a
concentration-dependent manner (15). These effects, if any, of
pentobarbital on determination of tissue glucose levels with
methylglucose would, however, be expected to be "dampened" by
1) simultaneous interference with
transport of glucose and methylglucose;
2) the slowing of metabolism by
pentobarbital, which tends to stabilize tissue glucose concentration at
higher levels; and 3) the factor in
Eq. A2 that includes
Kt as a sum with Cp. In fact, in our previous study
barbital sometimes damaged the blood-brain barrier but did not appear
to alter significantly the relationship between
C*e/C*p
and Ce (20), probably for the above reasons. Better "buffering" of inaccuracies in estimates of
the true values of S and
Kt by the ratio
(KtS + Ce)/ (Kt + Cp) in
Eq. A1 compared with that by the sum
(Kt + Cp) in Eq. A2 would be expected to contribute to superior
"goodness of fit" for predicted and measured values for
C*e/C*p
(Fig. 3) compared with glucose concentration (Fig. 4). Thus comparison
of Figs. 3 and 4 illustrates another important issue in modeling:
goodness of fit of theoretical to measured data can depend on the form of an equation derived from the model; poorer agreement between model-predicted and measured values can be apparent in one form of the
equation (i.e., Fig. 3) but not when the equation is rearranged and
tested (Fig. 4).
Estimation of intracellular water space.
Methylglucose is also used to determine intracellular water space in
cultured cells (e.g., Refs. 5, 9, 16, 17). Extracellular and
intracellular methylglucose concentrations are assumed to be equal at
equilibrium, and the intracellular water space is calculated from the
known extracellular methylglucose concentration and the measured
intracellular level of labeled methylglucose. This assumption may be
valid only if there is no glucose transporter and/or no
competition between glucose and any other substrate for the hexose
transporter. Omission of glucose from the test medium would, however,
cause energy failure, loss of ion homeostasis, and cell swelling.
Figure 4 shows that
C*e/C*p can vary over a twofold range when glucose levels are varied by supply
or demand. Thus failure to account for competition of methylglucose with glucose for transport into and from the cell could lead to errors
in estimates of intracellular water space.
Determination of the lumped constant of the DG method.
The lumped constant is the factor that converts the rate of
deoxyglucose phosphorylation to the
CMRGlc; it accounts for kinetic differences in the rates of transport and phosphorylation of the two
hexoses. When Ce exceeds 1 µmol/g, the value of the lumped constant is relatively stable, and
any errors in determination of local tissue glucose level with
methylglucose would therefore be expected to have a small effect on
calculated CMRGlc. For example, the magnitude of change in the value of the lumped constant is only
about one-tenth that of the corresponding change in tissue glucose
content in normoglycemic and hyperglycemic animals; an increase in
Ce level of 550% (e.g., from 1 to
5.5 µmol/g) causes the lumped constant to decrease by 40% (i.e.,
from 0.55 to 0.33) (6). Furthermore, compensatory mechanisms can
maintain Ce at or above the
"threshold level" at which changes in the lumped constant can
occur when metabolic demand is increased in brains of normoglycemic and
hyperglycemic rats. In the present study, a sustained two- to threefold
stimulation of CMRGlc did not
reduce local Ce below 0.8 µmol/g
so long as Cp exceeded ~7 mM
(Figs. 1 and 3 and Ref. 21).
The value of the lumped constant is most sensitive to incremental
changes in Cp and
Ce when the brain glucose level is
<1 µmol/g. Below this level, the value of the lumped constant rises abruptly and steeply, almost in proportion to the fall in
Ce. For example, when
Ce drops by 50% (e.g., from 1 to
0.5, or from 0.5 to 0.25 µmol/g), the lumped constant increases by
30-40% [i.e., from 0.55 to 0.77, or from 0.77 to 1.0, respectively (6); for graphic plots of this relationship, see Refs. 3,
6, 23, 24, 26, 28, and 29]. Thus errors in determination of
Ce would have the highest impact
on calculated CMRGlc when
Ce levels are in the hypoglycemic
range.
The
C*e/C*p
value is also most sensitive to changes in
Ce during hypermetabolic states,
particularly in the presence of hypoglycemia (6, 14; Figs. 1, 2, and
5), and methylglucose would therefore be most useful for detection of
changes in glucose level in the range that has the most significant
impact on the value of the lumped constant. Unfortunately, the extreme
conditions in which tissue glucose levels are the lowest are also those
in which estimates of glucose level are least reliable (Fig. 3). No
analytic method, however, is universally applicable to all possible
circumstances, and demonstration that local tissue glucose levels are
above or below the threshold level for uncertainty in the value of the lumped constant would help interpretation of results of metabolic studies under abnormal and pathophysiological states. The possibility of incurring errors in determination of
CMRGlc in the hypoglycemic state
suggests a simple strategy to avoid potential problems when CMRGlc must be
accurately determined under conditions in which neural pathways are
activated by physiological stimulation or mental tasks that would cause
large increases in cerebral metabolic rate. Unless a study is
specifically designed to examine conditions in which the brain glucose
level becomes limiting, fed or mildly hyperglycemic subjects should be
used so that compensatory mechanisms can maintain the
Ce near normal, thereby preventing
significant changes in Ce and
value of the lumped constant of the DG method.
 |
APPENDIX |
Theory
The rates of transport of substances that compete for transport across
the blood-brain barrier by the same transporter can be modeled by use
of simple competitive Michaelis-Menten kinetics. Thus the expression
for transport to and from the brain of tracer amounts of
[14C]methylglucose in
competition with the natural substrate, glucose, can be expressed as
follows. At equilibrium, rates of transport of methylglucose to
(v*in) and from
(v*out) the brain tissue
are equal
where
Kt and
K*t are Michaelis-Menten
half-maximal saturation constants for transport of glucose and
methylglucose, respectively;
Vt and
V*t are Michaelis-Menten
maximal velocity constants for transport of glucose and methylglucose, respectively; Ce,
C*e,
Cp, and
C*p are the hexose levels in brain (Ce,
C*e) and arterial plasma
(Cp and
C*p); and
S is the physical distribution space
for glucose and methylglucose in brain (i.e., brain water content
relative to that in plasma; see Refs. 1, 10, 11, 14). The expressions
1+(Cp/Kt)
and
1+(Ce/S)/Kt
take into account the competition of methylglucose with glucose by increasing the apparent value of
K*t for methylglucose.
At tracer concentrations, C*p and
C*e are approximately equal to zero.
Canceling and rearranging
|
(A1)
|
Rearranging
|
(A2)
|
These equations express the relationships among
Ce,
Cp, and
C*e/C*p,
with Kt and
S serving as constant parameters. The
transport of hexoses back and forth across the blood-brain barrier is
taken to be a process that obeys saturable kinetics according to the simplest Michaelis-Menten prediction. Our goal is to present a theoretical framework for understanding the relationships between C*e/C*p
and Ce in two distinct
circumstances: first, when Cp is clamped at a specific constant value (as in the current experiments), and
C*e/C*p
and Ce vary in response to changes
in metabolic demand; second, when the level of metabolic demand is
maintained at an essentially constant level [as in our previous
work (6, 14) and that of others (1, 11)] and
C*e/C*p
and Ce vary in response to changes
in glucose delivery, i.e., changes in
Cp. This framework is the basis
for comparison of calculated and experimentally determined relationships among Ce,
Cp, and
C*e/C*p
in the present study. Methods for determination of parameter values
from our data and used in these calculations are described in the
DISCUSSION and legend to Fig. 5. The
values used were as follows:
Kt (6.56 mM), S (0.89 ml/g), and
Km (0.063 mM).
The situation with constant supply is best described by
Eqs. A1 and A2 themselves. If
Cp is constant,
Ce is shown by
Eq. A2 to have a positive linear
dependence on
C*e/C*p
with a slope
(Kt+Cp) that increases as Cp increases.
Because the blood-brain transport barrier for hexoses is passive and
concentration driven, it follows that as the metabolic rate
becomes very small, Ce will
increase only to its limiting value of
SCp,
the hexose distribution space times the plasma concentration (please
see text that follows Eq. A4 below for
further explanation). This limiting value of
Ce defines the equilibrium
distribution space S, i.e.,
Ce/Cp = S. Substitution of this maximum into
Eq. A1 shows that the corresponding
maximum for
C*e/C*p
is equal to S. As metabolic rate
increases with Cp held
constant, Ce falls, ultimately
to its lower limiting value of zero, when all transported glucose is
consumed by tissue metabolism. Equation A1 predicts that
C*e/C*p
falls accordingly, until it reaches its smallest possible value of
KtS/(Kt+Cp)
in the limit of zero tissue glucose. Thus, in the situation of constant
plasma glucose concentration,
C*e/C*p
and Ce increase and decrease
together in response to changes in metabolic rate.
Equations A1 and A2 are not useful for illuminating the
relationship between
C*e/C*p
and Ce in the second situation, in
which we allow glucose delivery to vary while maintaining metabolic demand at some fixed level. This is because these two equations are
explicitly dependent on Cp, which
in those circumstances is not a fixed parameter but a variable. Rather,
we substitute for Cp a model
prediction for the Cp value that
would be expected to attain steady-state equilibrium with the given
value of Ce at some specific level
of metabolic demand. The resulting relationship, no longer explicitly
dependent on Cp, would then show
the mutual dependencies of
C*e/C*p
and Cp as demand is held fixed.
When glucose is in the steady state, the rate of transport from plasma
to brain is equal to the sum of the rate of return from brain back to
plasma and the rate of the (irreversible) phosphorylation reaction
|
(A3)
|
where
Vm and Km are the maximal
velocity and half-maximal saturation constraints for phosphorylation of
glucose by hexokinase, respectively. By dividing all terms
in Eq. A3 by the maximum velocity for
transport Vt, and
defining the ratio R = Vm/Vt
of the maximal velocities for phosphorylation and transport, we
get
|
(A4)
|
In this derivation, as in our previous report (14), changes
in metabolic demand are modeled only as changes in the ratio R. Conversely, the condition of fixed
metabolic demand is that R is a
constant. Equation A4 provides a
theoretical basis for the predictions made above, that
Ce increases only to its limit
SCp as R goes to zero, and that it
declines monotonically from that maximum as
R increases. As in the fixed-supply
case, the assumption is again made that half-saturation constants and
the distribution volume S do not vary.
For a given pair of values of Ce
and R, the equation predicts the
steady-state value of Cp to be
consistent with those values. If the right side of Eq. A4 is temporarily represented by the dummy variable
F
|
(A5)
|
then
|
(A6)
|
Substitution
of this expression into Eq. A1 above
yields
|
(A7)
|
Therefore
|
(A8)
|
Although this expression appears to be very complex, its
predictions are quite simple. The relationship between
C*e/C*p
and Ce for a given value of
R is essentially composed of two
distinct straight line segments. One segment describes their behavior
in the case of very low Cp values,
such that Ce is driven to such small values that hexokinase becomes unsaturated. If
Ce actually becomes small relative
to
KmS,
then the last term of the expression becomes negligible, and
C*e/C*p
is well approximated as
|
(A9)
|
As
supply is increased, the resulting level of tissue glucose
Ce saturates hexokinase, the
second term in the expression for
C*e/C*p
becomes independent of Ce, and the
last term becomes proportional to
Ce. The resulting prediction for
C*e/C*p
is again a straight line
|
(A10)
|
As
with Eqs. A1 and A2 we rearrange to get
|
(A11)
|
Because
the desaturation of hexokinase occurs only in the most extreme cases of
low supply or high demand, Eqs. A10 and A11 provide the practical working
relationships between
C*e/C*p
and Ce when demand is fixed and
supply varied. They are the counterparts of Eqs.
A1 and A2 above,
except with a parametric dependence on the demand parameter
R rather than the supply parameter
Cp. Note that in the circumstance
of fixed demand the slopes of their relationships are negative, with
one falling as the other increases and vice versa.
In the first situation (fixed supply and variable demand), the value of
Ce had a maximum imposed by the
fixed Cp value. As noted above,
even in the event of zero glucose utilization,
Ce could not rise above
SCp
because the transport barrier is passive. In the case of fixed demand,
however, Ce (at least in
principle) can be increased without limit, and therefore it is
interesting to remark on the consequent behavior of
Ce predicted by the current theory. For fixed demand and variable
Cp,
Ce rises in value as Cp is increased, and
C*e/C*p
falls accordingly. However, zero is the smallest physically allowable
value for the methylglucose distribution space, and thus
Ce does not increase without limit but is predicted by Eq. A11 to have
the maximum value
|
(A12)
|
For
low values of demand (small R), this
limiting value can become quite large; however, for the level of demand
determined in normal conscious rats in our previous report
(R = 0.34), the maximum value of
Ce is predicted to be the
surprisingly small value of ~15 µmol/g, as
Cp is increased without limit
(14).
 |
FOOTNOTES |
Address for reprint requests: G. Dienel, Dept. of Neurology, Slot
500, University of Arkansas for Medical Sciences, 4301 W. Markham St.,
Little Rock, AR 72205-7199.
Received 12 February 1997; accepted in final form 7 July 1997.
 |
REFERENCES |
1.
Buschiazzo, P. M.,
E. B. Terrell,
and
D. M. Regen.
Sugar transport across the blood-brain barrier.
Am. J. Physiol.
219:
1505-1513,
1970[Medline].
2.
Crane, P. D.,
L. D. Braun,
E. M. Cornford,
J. E. Cremer,
J. M. Glass,
and
W. H. Oldendorf.
Dose dependent reduction of glucose utilization by pentobarbital in rat brain.
Stroke
9:
12-18,
1978[Abstract].
3.
Crane, P. D.,
W. M. Pardridge,
L. D. Braun,
A. M. Nyerges,
and
W. H. Oldendorf.
The interaction of transport and metabolism on brain glucose utilization: a reevaluation of the lumped constant.
J. Neurochem.
36:
1601-1604,
1981[Medline].
4.
Cunningham, V. J.,
R. J. Hargreaves,
D. Pelling,
and
S. R. Moorhouse.
Regional blood-brain glucose transfer in the rat: a novel double-membrane kinetic analysis.
J. Cereb. Blood Flow Metab.
6:
305-314,
1986[Medline].
5.
Dessi, F.,
C. Charriaut-Marlangue,
and
Y. Ben-Ari.
Glutamate-induced neuronal death in cerebellar culture is mediated by two distinct components: a sodium chloride component and a calcium component.
Brain Res.
650:
49-55,
1994[Medline].
6.
Dienel, G. A.,
N. F. Cruz,
K. Mori,
J. E. Holden,
and
L. Sokoloff.
Direct measurement of the
of the lumped constant of the deoxyglucose method in rat brain: determination of
and lumped constant from tissue glucose concentrations or equilibrium brain:plasma distribution ratio for methylglucose.
J. Cereb. Blood Flow Metab.
11:
25-34,
1991[Medline].
7.
Dienel, G. A.,
N. F. Cruz,
K. Mori,
and
L. Sokoloff.
Acid lability of metabolites of 2-deoxyglucose in rat brain: implications for estimates of kinetic parameters of deoxyglucose phosphorylation and transport between blood and brain.
J. Neurochem.
54:
1440-1448,
1990[Medline].
8.
Dienel, G. A., H. Nakanishi, N. F. Cruz, and
L. Sokoloff. Determination of local brain glucose concentration
from the brain:plasma methylglucose distribution ratio: influence of
glucose utilization rate. J. Cereb. Blood Flow
Metab. 11, Suppl. 2:
S581, 1991.
9.
Foulkes, E. C.,
and
S. Blanck.
3-O-Methylglucose as a probe of cytoplasmic volume.
Life Sci.
54:
439-444,
1994[Medline].
10.
Gjedde, A.
Calculation of cerebral glucose phosphorylation from brain uptake of glucose analogs in vivo: a re-examination.
Brain Res. Rev.
4:
237-274,
1982.
11.
Gjedde, A.,
and
N. H. Diemer.
Autoradiographic determination of regional brain glucose content.
J. Cereb. Blood Flow Metab.
3:
303-310,
1983[Medline].
12.
Gjedde, A.,
and
M. Rasmussen.
Pentobarbital anesthesia reduces blood-brain glucose transfer in the rat.
J. Neurochem.
35:
1382-1387,
1980[Medline].
13.
Hawkins, R. A.,
A. M. Mans,
D. W. Davis,
J. R. Viña,
and
L. S. Hibbard.
Cerebral glucose use measured with [14C]glucose labeled in the 1, 2, or 6 position.
Am. J. Physiol.
248 (Cell Physiol. 17):
C170-C176,
1985[Abstract/Free Full Text].
14.
Holden, J. E.,
K. Mori,
G. A. Dienel,
N. F. Cruz,
T. Nelson,
and
L. Sokoloff.
Modeling the dependence of hexose distribution volumes in brain on plasma glucose concentration: implications for estimation of the local 2-deoxyglucose lumped constant.
J. Cereb. Blood Flow Metab.
11:
171-182,
1991[Medline].
15.
Honkanen, R. A.,
H. McBath,
C. Kushmerick,
G. E. Callender,
S. F. Scarlata,
J. D. Fenstermacher,
and
H. C. Haspel.
Barbiturates inhibit hexose transport in cultured mammalian cells and human erythrocytes and interact directly with purified GLUT-1.
Biochemistry
34:
535-544,
1995[Medline].
16.
Kletzien, R. F.,
M. W. Pariza,
J. E. Becker,
and
V. R. Potter.
A method using 3-O-methylglucose and phloretin for the determination of intracellular water space of cells in monolayer culture.
Anal. Biochem.
68:
537-544,
1975[Medline].
17.
Latzkovits, L.,
H. F. Cserr,
J. T. Park,
C. S. Patlak,
K. D. Pettigrew,
and
A. Rimanoczy.
Effects of arginine vasopressin and atriopeptin on glial cell volume measured as 3-MG space.
Am. J. Physiol.
264 (Cell Physiol. 33):
C603-C608,
1993[Abstract/Free Full Text].
18.
Lowry, O. H.,
and
J. V. Passonneau.
A Flexible System of Enzymatic Analysis. New York: Academic, 1972.
19.
Mason, G. F.,
K. L. Behar,
D. L. Rothman,
and
R. G. Shulman.
NMR determination of intracerebral glucose concentration and transport kinetics in rat brain.
J. Cereb. Blood Flow Metab.
112:
448-455,
1992.
20.
Nakanishi, H.,
N. F. Cruz,
K. Adachi,
L. Sokoloff,
and
G. A. Dienel.
Influence of glucose supply and demand on determination of brain glucose content with labeled methylglucose.
J. Cereb. Blood Flow Metab.
16:
439-449,
1996[Medline].
21.
Newman, G. C.,
F. E. Hosped,
B. Maghsoudlou,
and
C. S. Patlak.
Simplified brain slice glucose utilization.
J. Cereb. Blood Flow Metab.
16:
864-880,
1996[Medline].
22.
Otsuka, T.,
L. Wei,
D. Bereczki,
V. Acuff,
C. Patlak,
and
J. Fenstermacher.
Pentobarbital produces dissimilar changes in glucose influx and utilization in brain.
Am. J. Physiol.
261 (Regulatory Integrative Comp. Physiol. 30):
R265-R275,
1991[Abstract/Free Full Text].
23.
Pardridge, W. M.,
P. D. Crane,
L. J. Mietus,
and
W. H. Oldendorf.
Nomogram for 2-deoxyglucose lumped constant for rat brain cortex.
J. Cereb. Blood Flow Metab.
2:
197-202,
1982[Medline].
24.
Pardridge, W. M.,
P. D. Crane,
L. J. Mietus,
and
W. H. Oldendorf.
Kinetics of regional blood-brain barrier transport and brain phosphorylation of glucose and 2-deoxyglucose in the barbiturate-anesthetized rat.
J. Neurochem.
38:
560-568,
1982[Medline].
25.
Pontén, U.,
R. A. Ratcheson,
L. G. Salford,
and
B. K. Siesjö.
Optimal freezing conditions for cerebral metabolites in rats.
J. Neurochem.
21:
1127-1138,
1973[Medline].
26.
Schuier, F.,
F. Orzi,
S. Suda,
G. Lucignani,
C. Kennedy,
and
L. Sokoloff.
Influence of plasma glucose concentration on lumped constant of the deoxyglucose method: effects of hyperglycemia in the rat.
J. Cereb. Blood Flow Metab.
10:
765-773,
1990[Medline].
27.
Siesjö, B. K.
Brain Energy Metabolism. New York: Wiley, 1978, p. 117-120.
28.
Sokoloff, L.,
G. A. Dienel,
N. F. Cruz,
and
K. Mori.
Autoradiographic methods in pathology and pathophysiology.
In: Pharmacology of Cerebral Ischemia, edited by J. Krieglstein,
and H. Oberpichler. Stuttgart, Germany: Wissenschaftliche Verlagsgesellschaft, 1990, p. 3-21.
29.
Sokoloff, L.,
M. Reivich,
C. Kennedy,
M. H. Des Rosiers,
C. S. Patlak,
K. D. Pettigrew,
O. Sakurada,
and
M. Shinohara.
The [14C]deoxyglucose method for the measurement of local cerebral glucose utilization: theory, procedure, and normal values in the conscious and anesthetized albino rat.
J. Neurochem.
28:
897-916,
1977[Medline].
30.
Suda, S.,
M. Shinohara,
M. Miyaoka,
G. Lucignani,
C. Kennedy,
and
L. Sokoloff.
The lumped constant of the deoxyglucose method in hypoglycemia: effects of moderate hypoglycemia on local cerebral glucose utilization in the rat.
J. Cereb. Blood Flow Metab.
10:
499-509,
1990[Medline].
31.
Veech, R. L.,
R. L. Harris,
D. Veloso,
and
E. H. Veech.
Freeze-blowing: a new technique for the study of brain in vivo.
J. Neurochem.
20:
183-188,
1973[Medline].
32.
Youn, J. H.,
J. K. Kim,
and
G. M. Steil.
Assessment of extracellular glucose distribution and glucose transport activity in conscious rats.
Am. J. Physiol.
268 (Endocrinol. Metab. 31):
E712-E721,
1995[Abstract/Free Full Text].
AJP Endocrinol Metab 273(5):E839-E849