Splanchnic retention of intraduodenal and intrajejunal glucose
in healthy adults
G.
Livesey1,
P. D. G.
Wilson2,
M. A.
Roe1,
R. M.
Faulks1,
L. M.
Oram1,
J. C.
Brown1,
J.
Eagles1,
R. H.
Greenwood3, and
H.
Kennedy4
Departments of 1 Nutrition,
Diet, and Health and 2 Food
Biophysics, Institute of Food Research, Norwich NR4 7UA; and
Departments of 3 Medicine and
4 Gastroenterology, Norfolk and
Norwich Hospital, Norwich NR1 3SR, United Kingdom
 |
ABSTRACT |
Estimates of the
spanchnic retention and appearance in the systemic circulation of
orally administered glucose vary among laboratories even after recently
identified sources of error have been accounted for [Livesey, G., P. D. G. Wilson, J. R. Dainty, J. C. Brown, R. M. Faulks, M. A. Roe, T. A. Newman, J. Eagles, F. A. Mellon, and R. Greenwood. Am.
J. Physiol. 275 (Endocrinol. Metab. 38):
E717-E728, 1998]. We questioned whether, in healthy humans,
D-glucose delivered
intraluminally to the midjejunum appeared systemically as extensively
as that delivered intraduodenally. Subjects were infused over a period
of 90 min with 50 g of glucose in 1 liter of isotonic saline
(incorporating 0.5 g
D-[13C6]glucose)
per 70 kg of body weight. Infusions were via enteral tubes terminating
~15 and 100 cm postpylorus. The systemic appearance of glucose was
monitored by means of a primed-continuous intravenous infusion of
D-[6,6-2H2]glucose.
Whereas 98 ± 2% (n = 7) of the
duodenally infused glucose appeared in the systemic circulation, only
35 ± 9% (n = 7) of midjejunally
infused glucose did so, implying that 65 ± 9% was retained in the
splanchnic bed. Either glucose was less efficiently absorbed at the
midintestinal site or hepatic glucose sequestration was increased
10-fold, or both. The proximal intestine plays a key role in the delivery of glucose to the systemic
circulation, and the distal intestine potentially delivers more glucose
to the liver.
stable isotopes; absorption; metabolism; modeling
 |
INTRODUCTION |
LITTLE IS KNOWN about the systemic appearance of
glucose that arrives in the distal intestinal lumen, yet this
potentially happens during the consumption of slowly digestible
starches, during the coingestion of either motility or osmotic agents,
and when pancreatic secretions are inadequate. Moreover, the distal small intestine is important in individuals who have had their proximal
intestine surgically removed for health reasons. The extent to which
orally administered glucose is absorbed and escapes hepatic
sequestration to reach the systemic circulation in humans can be
determined using dual isotope methodology (3, 9, 11, 13). In people
with a healthy intact small intestine, experimentally determined values
range from 70 to 95% or more (for an analysis see Ref. 9). In many
instances, low estimates can be explained quantitatively by choice of a
too-small effective-pool volume, through which the glucose becomes
distributed after absorption, and a too-infrequent blood sampling for
adequate kinetic analysis, particularly in the early, rapid phase of
glucose absorption (9). But these did not explain all the low systemic
appearance estimates published that followed the use of dual isotope
methodology. Known physiological causes of low systemic glucose
appearances in healthy people are few. Potential causes are either
incomplete absorption of glucose, which is then either retained
intraluminally or fermented after passage to the large intestine, or
the sequestration of glucose during its first passage through the liver
to which it is first directed via the portal vein. The potential for
poor absorption exists if glucose can escape the proximal small
intestine, where the density of glucose transporters is high relative
to the distal small intestine (2, 4). Poor absorption in the distal
section of the small intestine would happen only if glucose transporters were rate limiting. It was therefore of interest to test
the hypothesis that the extent of systemic appearance of glucose
depends on the site at which glucose is delivered in the small
intestine.
To determine whether the disposition of glucose depends on the site of
delivery, we intubated healthy individuals to distances from 15 cm
postpylorus, which may be defined as intraduodenal, to between 85 and
120 cm postpylorus, which may be defined as midjejunal (6), and we
monitored the utilization of glucose delivered to these sites using the
dual stable isotope approach (9). An APPENDIX is given to facilitate an
understanding of the modeling methodology used in the oral glucose load
dual stable isotope paradigm, to avoid confusion with other
experimental paradigms and to give background, details of augments, and
important aspects of the glucose modeling methodology, which if
included in the body of the paper would cause diversion from the
central thrust.
 |
METHODS |
Participants.
Nine healthy volunteers with no history of gastrointestinal disease
were recruited. Six were female, three were male; they were 43 ± 11 (27-57) yr old, weighed 71 ± 13 (48-91) kg, and
had a body mass index of 24 ± 3 (19-28)
kg/m2. They ate their habitual
diets, were weight stable between recruitment and performance of
investigations, and were nonmedicated. Informed written consent was
provided by all volunteers, and the study was approved by the ethics
committees of the Institute of Food Research and the Norfolk and
Norwich Health Authority.
Experimental design.
Volunteers were oroenterally intubated 48 h before investigations. The
enteral tube was 1.5 mm OD, 0.75 mm ID, PVC (Portex, Hythe, UK) fitted through a terminal pear-shaped 10-g stainless steel
weight (Institute of Food Research, Norwich, UK). Food and nonalcoholic
drinks continued normally while the tube was being positioned and was
in place. An internal length of tube equal to the
mouth-to-ear-to-2nd-rib distance plus 15 cm was placed for
intraduodenal delivery (15 cm postpylorus), and this length of tube
plus ~85 cm was placed for the midjejunal site (100 cm postpylorus).
Entry into the duodenum was ascertained with a neutral bile-containing
aspirate and stethoscopic location of air delivered through and bubbled
from the tube. The midjejunal location was established by fluoroscopy
(BUPA Norwich, Colney, Norwich, UK). From the pool of nine volunteers,
seven were duodenal and seven were midjejunal. For those who were
intubated twice, the procedures were
6 wk apart.
In the 12 h before each investigation, the subjects had no
food and only water to drink. The volunteers rested overnight
before being seated for 10 h in a recliner chair (Parker Knoll, UK). An
antecubital vein and a subsequently heated (41°C) dorsal hand vein
were cannulated (18-g Teflon) and kept patent with physiological saline. Pyrogen-free
D-[6,6-2H2]glucose
(99 mol% enrichment, C/D/N Isotopes, K&K Greeff, Croydon, UK) was
administered as a primed (500 mg, 10 ml aqueous solution) continuous (6 mg/min as a 68.5 g/l aqueous solution) infusion into the antecubital
vein, starting at ~0900, which is denoted time
0 in RESULTS. After 2 h, we enterally infused 50 g
D-glucose [labeled with
500 mg
D-[13C6]glucose
(99 mol% enriched, also C/D/N Isotopes)] in 1 liter of isotonic
NaCl over a period of 90 min. Arterialized venous blood was drawn into
tubes from the heated hand initially at 15-, then at 30-, and then at
60-min intervals, as indicated in Figs. 1-6.
Glucose and isotope analysis.
Plasma glucose was determined by use of hexokinase, and plasma glucose
isotopes were determined on butylboronic acid derivatives by use of
gas-chromatography electron impact mass spectrometry. The details of
these procedures and the precision of the methods were as we described
previously (9).
Rate of appearance calculations and statistics.
The rate of appearance (Ra) of
enterally intubated glucose was estimated using a one-compartment model
that has been identified to be suitable in the present experimental
paradigm (see Ref. 9 and APPENDIX)
and applies an effective glucose distribution volume of 230 ml/kg body
weight (9). Details of this approach and justification of the use of
the one- compared with a two-compartment model in the present
experimental paradigm are as given before (9) (see also
APPENDIX). Computations were
performed without interpolation or data smoothing. Glucose
concentrations and tracer-to-tracee (tracer-tracee) ratios are
presented to facilitate an assessment of whether modeling would under-
or overestimate a treatment effect and for comparison of the present
constant tracer approach with a previously published variable tracer
approach to estimating Ra (17).
Individual observations are given as means and population sample
standard errors of the mean. Significance of difference between population sample means was tested using an unpaired Student's t-test
(n = 7).
 |
RESULTS |
Model-independent results.
Figure 1 shows the occurrence in
arterialized plasma of glucose that originated from intubation into the
duodenum and midjejunum and that was traced with
D-[13C6]glucose.
For the same amount of glucose administered (50 g · 90 min
1 · 70 kg body weight
1), the
area under the curve fell (P < 0.05, unpaired t-test) by 57 ± 10% on
change of infusion site from the duodenum to the midjejunum.

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Fig. 1.
Systemic occurrence of duodenally ( ) and midjejunally ( ) infused
glucose. Glucose (50 g/70 kg body wt) was infused over a 90-min period
starting at 120 min and was traced with
D-[13C6]glucose.
Values are means ± SE (n = 7). Areas
under the curve were significantly different
(P < 0.05, unpaired Student's
t-test).
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Model-dependent results.
The
D-[13C6]glucose
infused into the duodenum rapidly appeared in the systemic circulation
(Fig. 2). The
Ra was very nearly equal to the
enteral infusion rates in all seven participants, suggesting that the
infusion rate was rate limiting for both glucose absorption and
systemic Ra. On termination of the
enteral infusion, appearance in the systemic circulation decelerated to
a plateau, when 98 ± 2% of the administered glucose appeared to
have passed systemically. The results with all individuals were very
similar.

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Fig. 2.
Cumulative systemic appearance of
D-[13C6]glucose
in arterialized plasma after infusion into the duodenum (~15 cm
postpylorus). Bold line, rate of infusion (50 g · 70 kg body
wt 1 · 90 min 1). There are 7 data
curves, 1 for each participant. Plateau mean was 98 ± 2%
of enteral infusion.
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Infusion of the
D-[13C6]glucose
into the midjejunum gave different results (Fig.
3). Systemic appearance was always less
than the infusion rate. Ra values
differed substantially between individuals, as did the level of the
eventual plateau that signaled a cessation of appearance in the
systemic circulation. Cessation of the infusion was not followed by an
immediate fall in systemic appearance rate, and the time at which the
plateau began tended to be inversely related to the initial
Ra of the administered glucose. By
contrast with the intraduodenal infusion, in which most glucose passed into the systemic circulation, a mean of only 35 ± 9% of
midjejunally administered glucose passed systemically, and the
remainder was retained in the intestinal lumen or sequestered by the
liver during first pass through this organ.

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Fig. 3.
Cumulative systemic appearance of
D-[13C6]glucose
in arterialized plasma after infusion into the midjejunum (~100 cm
postpylorus). Bold line, rate of infusion (50 g · 70 kg body
wt 1 · 90 min 1). There are 7 data
curves, 1 for each participant. Plateau mean was 35 ± 9%
of enteral infusion.
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The average fall in the (model-dependent) systemic glucose appearance
on change of infusion site from the duodenum to the midjejunum was 65 ± 9%, similar to the average fall in (model-independent) systemic
occurrence of glucose (57 ± 10%).
Not only was the systemic appearance after midjejunal infusion
substantially lower than after the duodenal infusion, but it varied
with the length of enteral tube that was passed (Fig.
4). The fall in systemic appearance,
assessed by regression analysis, was 69 ± 8%/m, which was highly
significant (t = 8.7, P = 0.000002).

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Fig. 4.
Correlation of distance along small intestine and percentage of
enterally administered dose of
D-[13C6]glucose
that appears systemically. Correlation coefficient,
r2, 0.86; slope,
70 ± 8% (P = 0.00002) per meter
of intestine.
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Tracee concentrations and tracer-tracee ratios.
The model we used to estimate the
Ra of exogenous glucose after 50 g
of oral glucose was found to be accurate (±5% of glucose ingested)
compared with a two-compartment reality (9), and errors no greater than
this are expected for the present data (Figs. 2-4), because the
amounts of glucose administered were similar. Reasons for such small
errors are given in APPENDIX. Rates of
systemic appearance of exogenous glucose from the gut are difference
estimates from two sets of data modeling, one for nontracer total
glucose and one for endogenous glucose; thus enteral
Ra is equal to the nontracer total
Ra minus the endogenous
Ra. Onset of enteral infusion at
both sites in the gut decreased the occurrence of endogenous glucose
and elevated the tracer-tracee ratio used in calculations of endogenous
glucose Ra values (Fig.
5). This suggests that modeling error would
tend to overestimate rather than underestimate the endogenous glucose
Ra values, which in turn would
result in an underestimation (not overestimation) of the systemic
Ra values of enteral glucose. By
contrast, onset of enteral glucose infusion at both sites was
accompanied by a rise in the nontracer total glucose concentration and
a fall in the tracer-tracee ratio used in calculation of nontracer
total glucose Ra values (Fig.
6). This suggests overall underestimation
(rather than overestimation) of both nontracer total glucose and
enteral glucose Ra values. Thus
differences between the model system used to make rate estimates and
the real system caused the two sets of data modeling to introduce potential errors with the same sign, which add to underestimate the
systemic appearance of enteral glucose. The tracer-tracee ratios did
not change monotonically; this suggests that the errors would be balanced during return toward the initial steady-state tracer-tracee ratios, but by the end of the study the estimate of
glucose appearance (Figs. 2-4) would remain an underestimate. Variation in tracer-tracee ratios after duodenal infusions was greater
than after midjejunal infusions (Figs. 5 and 6), which suggests that
the difference observed in treatment on account of differences between
the model and the real system would be underestimated rather than
overestimated.

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Fig. 5.
Systemic occurrence of nontracer total glucose and associated
tracer-to-tracee ratio (TTR) after duodenal ( ) and midjejunal ( )
glucose infusion. Glucose (50 g/70 kg body wt) was infused over a
90-min period starting at 120 min and was traced with
D-[13C6]glucose.
Values are means ± SE (n = 7).
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Fig. 6.
Systemic occurrence of endogenous (hepatic) glucose and associated TTR
after duodenal ( ) and midjejunal ( ) glucose infusion. Glucose (50 g/70 kg body wt) was infused over a 90-min period starting at 120 min
and was traced with
D-[13C6]glucose.
Values are means ± SE (n = 7).
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DISCUSSION |
We show for the first time that glucose delivered into the midjejunum
of healthy adult humans is very slowly and incompletely transferred to
the systemic circulation, whereas there is rapid and nearly complete
transfer of glucose administered intraduodenally. Our definition of a
midjejunal site requires more precise definition. It was ~1 m beyond
the pylorus. This accords with the duodenum being the first 25 cm and
the jejunum being the next 2 m of small intestine in a total length in
vivo of 3-4.5 m (6). Subsequent studies in two of our volunteers
showed them to have 3-m-long small intestines in vivo when measured by
intubation and fluoroscopy. These lengths contrast with
the generalization that the small intestine is ~6 m long, which is
probably so only after muscular tone is lost postmortem.
The rate and extent of glucose appearance systemically depend on the
rate of glucose absorption less the rate at which glucose enters the
liver during its first pass through this organ while in blood on its
way from the gut to the systemic circulation. The 98 ± 2%
(n = 7) systemic appearance of
intraduodenally infused glucose is consistent with our previous finding
of 97 ± 3% (n = 22) appearance of
50 g oral glucose/70 kg body weight, and the remainder is not
significantly different from a 2-8% first-pass sequestration of
glucose by the liver (3, 11, 12). As discussed before (9), the
accumulation of recently absorbed oral glucose in the liver appears to
be largely dependent on the subsequent 40 or so repasses during the
course of the absorptive period.
Consideration needs to be given to the question of how glucose becomes
retained in the liver as glycogen. Magnetic resonance spectroscopy
(MRS) studies show that considerable accumulation of
glucose in the liver occurs after oral carbohydrate ingestion, some
20% of the carbohydrate of the meal (17). The present and previous
stable isotope data and some previous radioisotope and arteriovenous
difference data (see Ref. 9) suggest that probably no more than 5%
enters directly after oral and duodenal glucose. Most of the absorbed
glucose seems to be available to muscle, where it may be stored as
glycogen, with the liver accumulating glucose also from the systemic
pool to reach the 20% or more deposited in the liver after a meal
(17). This may have important implications for the way we think about
regulation of the distribution of glucose between liver and muscle
stores.
A possibility exists that, after a meal, more of the carbohydrate
reaches the midjejunum with a higher proportion being sequestered by
the liver, which may explain both the lower systemic appearance of
distally infused glucose (Figs. 3 and 4) and the higher (>5%) accumulation of glucose as liver glycogen after a high-carbohydrate meal (17). Unfortunately, MRS studies would not resolve the question of
what proportion of glucose from the gut enters the liver direcly
compared with indirectly after passage via the hepatic and systemic
circulation. However, MRS studies would enable a distinction to be made
between accumulation in the liver of substantial amounts of glucose
from the distal intestine and retention within the intestinal lumen;
such a distinction merits investigation.
The systemic appearance of midjejunally infused glucose was far from
complete, either because of incomplete absorption or because the
first-pass hepatic glucose sequestration was substantial, or both. An
increase in hepatic glucose sequestration with increasing distance
along the small intestine would have important implications for the
understanding and potential control of blood glucose concentrations during the absorptive period and would require intraluminal
glucose-mediated neurohormonal mechanisms to facilitate, for example,
hepatic glycogenesis. To our knowledge there are no candidate
mechanisms. We do not believe hepatic glucose sequestration alone can
account for all the glucose that failed to reach the systemic
circulation. If it is assumed that all the intrajejunally infused
glucose was absorbed and that the liver was responsible for the
nonappearance systemically, the first-pass hepatic sequestration would
have been, on average, 65 ± 8% of each pass. Such an extraction
rate would likely also apply to glucose entering the liver from the systemic circulation. At a blood flow rate of 1 l/min through liver, an
approximate basal value, a 65% extraction rate, would have completely
drained the free glucose from the systemic pool, which could not and
did not happen. It follows that incomplete absorption accounts for at
least a part of the nonsystemic appearance of the intrajejunal glucose.
Should incomplete absorption explain most of the low systemic
appearance, the glucose absorption capacity in healthy humans would
vary markedly along the length of the first 120 cm of the small
intestinal tract, probably due to changes in the density of glucose
transporters, as observed in animal studies (2, 4).
A note is warranted about the accuracy of the present methodology to
allay certain misconceptions before a conclusion can finally be drawn.
It is well established that one-compartment modeling of single
isotope-monitored glucose metabolism leads to negative estimates of
hepatic glucose production when exogenous (intravenous) glucose
infusion rates are known (8). It should not be thought that the
dual-isotope approach as used at present has the same result. Modeling
using the dual-isotope approach after oral glucose tends to
overestimate endogenous (hepatic) glucose production (9, 10) for
reasons explained in APPENDIX. Thus
the two experimental paradigms should not be confused.
The dual-isotope approach appears particularly good for estimating
endogenous (hepatic) glucose production in the present experimental
paradigm, provided the glucose distribution volume used is close to
total, VT, as demonstrated in
practice (9) and with theory
(APPENDIX), but is in substantial
error when a fractional or partial
VT
(pVT) is used, where
fraction (p) = 0.65 as shown in practice (11) and with
theory (1, 10). It is of some concern that such errors are evident in
the majority of studies on the systemic appearance of oral glucose (see
review in Ref. 9). The explanation for the present result having
adequate accuracy is that a multicompartment reality collapses into a
single compartment with a volume equal to
VT when glucose concentrations and
tracer-tracee ratios change reasonably slowly
(APPENDIX). Expressed differently,
volume and structure errors
(ev and
es,
respectively), as defined by Cobelli et al. (1), finally balance at
zero in such a collapsed reality
(APPENDIX). Lowering of the volume
to below VT, such as when
pVT is used, only makes
the balance of structure and volume errors worse (by ignoring the
second compartment), leading to underestimation of exogenous glucose
production.
For comparison of present with previous tracer-tracee ratios, Taylor et
al. (17) used a variable tracer infusion to stabilize the ratio for
endogenous glucose with residual fluctuation within a twofold range
(75-150% basal), whereas in the present study, with a constant
isotope infusion, the range of means was not more than threefold
(100-300% basal). It is noteworthy that, at any particular
glucose concentration, the percentage rise in this ratio has less
impact on the result than a percentage fall [a consequence of the
term 1
(a2/a1)
when a2 is
delayed a1; see Eq. A6b in
APPENDIX]. Although this ratio
seems to change markedly in the present study, it is not that much more
variable than is achievable with a variable infusion, and we must
consider that the changes found extend throughout the pool volume of
230 ml/kg body wt. Keeping this tracer-tracee ratio low is particularly difficult, because endogenous glucose concentrations fall toward zero,
so the ratio could easily reach infinity. Nevertheless, rises in this
ratio on this account have only small impact on error, because at zero
concentration, errors are also zero (see APPENDIX). Estimates of glucose
Ra from the gut in the present
paradigm are not as good as those estimated for endogenous glucose
production (9). Nevertheless, in the present study, as in others (9), we expect accuracy of exogenous glucose production to be within ±5% of the total exogenous glucose load (at any given time and given
50 g intake) compared with a two-compartment reality (10, 11).
In other circumstances, greater errors are known and many varied
attempts have been made at error minimization (see
APPENDIX). Furthermore, the rise to
plateau and end point of our endogenous glucose appearance estimates
after duodenal glucose were close to expectations (95%) on the basis
of arteriovenous difference studies (3, 11, 12), which adds validity to
our findings. The limit would of course be 100%, which gives little
scope for error in the present and previous (9) data because of the
model's underestimation of systemic appearance of exogenous glucose
(as "real" values would then be impossibly >100%).
A further potential misconception is that dilution of tracer and tracee
in the portal vein by exogenous glucose will lead to errors in
Ra , which does not happen for
systemic Ra but does for whole
body Ra (and disappearance rate).
The difference is due to the rate of first-pass hepatic glucose
sequestration from the gut (as noted in
APPENDIX).
We conclude that the methodology used for estimating the systemic
appearance of exogenous glucose is reasonably robust, giving after
duodenal glucose infusion an Ra
and end point close to but less than the infusion rate, in keeping with
expectations based on arteriovenous difference studies. A substantial
fall in exogenous glucose Ra
results from the delivery of glucose only a small distance (1 m)
distally along the small intestine, and modeling errors, although
considered to be small, tend to underestimate this difference. Hence
the proximal intestine plays a key role in the delivery of glucose to
the systemic circulation, and the distal intestine potentially delivers
more glucose to the liver, or, equally surprisingly, retains it within
the intestinal lumen or carries the glucose to the large intestine in
considerable amounts.
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APPENDIX |
Approaches to error minimization.
The real metabolic system is complex, and, by definition, models only
approximate the complexity. Differences between real and model systems
result in real errors that may be time variant [es(t)].
Since Steele (15) introduced the one-compartment model (Eq. A1a) to estimate a
time-dependent glucose Ra
[Ra(t)],
at least five approaches have been used to minimize these errors.
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(A1a)
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First,
effective parameter estimates have been used. For example, an invariant
effective pool volume (VS, as
shown in Eq. A1a) is a fraction
(p) of the original total glucose distribution volume
(VT) such that
VS = pVT in Steele's
one-compartment model and, importantly, wherein the size of
VS depends on the experimental paradigm. Second, a time-variable
VS (or p) has been used
in place of VT (or
pVT) in the
one-compartment model to eliminate apparent time dependency (5). Third,
more complex models have been introduced with invariant volumes (10,
14, 16). Fourth, experimental design has been changed (by use of
variable tracer infusions) to stabilize the tracer-tracee ratio
[a(t)] and its
derivative (
) (8, 17),
and so to make the Ra estimates
independent of model structure and volumes (and by extrapolation,
independent of the structure of the real system) (7). Fifth, both
variable tracer infusions and more complex models have been used (17). The fifth arises because tracer-tracee ratios are impossible to stabilize exactly, and so Ra
estimates are always model dependent and yield real errors. In all
cases, the Ra estimates have real errors, which by definition cannot be quantified exactly, but upper
bounds to the size of the error can be estimated (10, 11), and, short
of this, the direction of the error can be elucidated to uncover
whether a treatment effect is under- or overestimated because of
differences in real errors between treatments.
Multicompartment reality.
In the constant tracer infusion dual-isotope paradigm, three rate
estimates are possible: rate estimates for endogenous, exogenous, and
total glucose. All three rates differ and can have time-dependent real
errors of differing size and direction, even when they are applied to
the same model. Such errors arise from oversimplification of the
multicompartment reality. The most general multicompartment reality is
describable in modeling terms, as was done by Cobelli et al. (1) by
Eq. A2
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(A2a)
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(A2b)
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(A2c)
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(A2d)
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(A2e)
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R0(t)
is the non-steady-state term that describes the
Ra when the tracer-tracee ratio,
a, is constant or, as usually happens in practice, changes very slowly. When
a changes more than this but not
rapidly, a term including the derivative
da/dt =
is required to retain
accuracy, as in
R1(t)
(Eq. A2c), and so
R0(t)+R1(t) describes the one-compartment model in the nonsteady state, but only
when changes in a are not rapid and
when V1 approaches
VT (as will be described). The sum
R0+R1
appears invalid when the tracer-tracee ratio
a changes rapidly, revealing
that the real system is at least better described by a two-compartment
model in which
Ra(t) = R0(t)+R1(t)+R2(t),
and the tracer-tracee ratio is
a1 and
a2 in
compartments 1 and
2, respectively, and
k21,
V2, and
C2 are the rate parameters from
compartment 2 to
compartment 1, the volume of
compartment 2, and the concentration
of tracee in compartment 2,
respectively. Noncompartmental analysis reveals that three kinetics may
still better maintain accuracy should a change very rapidly. Addition of a
third or more nth compartment (also
connected to the first) requires addition of an
nth term that is identical in
structure to term
R2(t)
for compartment 2, and so the nature
and direction of the real error through omitting the
nth compartment in the model are the
same as for omitting compartment 2. As
will be described, the sizes of
V1,
V2, and Vn are model dependent. For the
one-, two-, and three-compartment models, respectively,
V1
VT,
V1+V2
VT, and
V1+V2+V3
VT. The approximations (
)
arise because volume estimates are obtained by noncompartmental
analysis simultaneously with estimates of the rate parameters
(k), such that errors in the
determination of V should be balanced by errors in the determination of
k.
Collapsing the multicompartment reality into a one-compartment
model.
Users of one-compartment modeling almost invariably use a glucose
distribution volume VS less than
VT. It is of interest, therefore,
to show whether this affects the ability of the one-compartment model
to represent a multicompartment reality. A difficulty with multicompartment models is that only compartment
1 is accessible. Nevertheless, this may be overcome
with complicated mathematics. As shown by Mari (10),
R2(t)
(Eq. A2d) is given by convolution integrals
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(A3a)
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(A3b)
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As also noted by
Mari (10), when
C1(t)
and
change slowly,
g(t), an estimate of
C2(t),
approximately equals
C1(t),
and the result of the integral in Eq. A3a approximately equals
C1(t)
, and so Eq. A3a collapses into
Eq. A4a
|
(A4a)
|
It
follows, therefore, that in a two-compartment reality when
C1(t)
and
1
change slowly, the sum
R0(t)+R1(t)+R2(t)
is given by the sum of results from Eqs. A2b,
A2c, and A4a. In this
sum, the last two terms,
R1(t)+R2(t),
simplify to Eq. A5a, which has the same form as in the one-compartment model but in which the volume term
is greater because V1 is replaced
by
V1+V2.
|
(A5a)
|
The
arguments applied here to the second compartment would apply equally to
the nth compartment, and so, provided
C1(t)
and
1
change sufficiently slowly, the multicompartment reality can be
represented by a one-compartment model [and if
C1(t)
and
1 do not change at all or change very slowly, a zero compartmental analysis is sufficient, as in Eq. A2b,
R0]. Demonstration of the adequacy of the one-compartment approach under these circumstances is
the nearly identical result for the one- and two-compartment models for
both endogenous and exogenous glucose
Ra values when, in the
one-compartment model, the glucose distribution volume used was
V1+V2
and when the source of exogenous glucose was 50 g glucose/70 kg body
weight and when the tracer infusion was constant, as opposed to
variable (9). When V1 alone is
used in the one-compartment model, estimates of endogenous glucose
appearance are too high, and estimates of both total and exogenous
glucose appearance are too low, as was demonstrated under essentially
identical conditions by Mari et al. (11). The similarity in
Ra estimates with the two-compartment model and the one-compartment model with
VT = V1+V2
for the two compartments is evidence of a relatively low rate of change
in both
C1(t)
and
1.
The absorption of 50 g glucose/70 kg body weight, as in the present
study, evidently perturbs
C1(t) and
1
relatively slowly in the context of compartmental modeling, at least in
healthy people.
Balance of volume and structure errors in a collapsed
multicompartment reality.
Real errors
er(t) for
a one-compartment model have been defined by Cobelli et al. (1) by
assuming that a two-compartment model accurately describes the real
system, which may be represented as
|
(A6a)
|
|
(A6b)
|
|
(A6c)
|
Equation A6b, resulting in
es(t),
is identical to Eq. A2c, resulting in
R2(t)
[i.e.,
es(t) = R2(t)];
hence, when
C1(t)
and
1 change slowly, the structure error collapses, as did
R2(t)
from Eq. 3, a and
b, to Eq.
4a, to give Eq. A7a
|
(A7a)
|
When
VS is chosen to be
VT and
VT = V1+V2,
it follows that VS
V1 in Eq. A6c is equal to
V2, and so the equations for
es(t) and
ev(t)
become equal but of opposite sign. Thus when
VS = VT = V1+V2,
and
C1(t)
and
1
change slowly,
es(t)
ev(t)
and
er(t) is approximately zero.
The same arguments apply for the nth
compartment, provided that
V1+V2...+Vn = VT. It follows that when
C1(t) and
1
change slowly, as in the present experimental paradigm, a one-compartment model that uses a volume unequal to
VT, such as when it is
pVT, results in a modeling error,
of which there are many examples in the literature.
Mistransposition of the experimental paradigm.
It must not be thought that the present study result would suffer from
errors causing negative estimates of endogenous or hepatic glucose
production, and hence overestimation of exogenous glucose appearance.
It has been hypothesized that estimates of endogenous glucose
production can be derived as the difference in total glucose
Ra calculated using a constant
tracer infusion, a one-compartment model, and known rates of unlabeled
exogenous glucose infusion, as in the early hot euglycemic clamp. In
this experimental paradigm, it is known that
1) the overall error is large,
2) the direction of the error causes
endogenous glucose production to be underestimated [the so-called
"negative hepatic glucose production problem" (5, 8)], and
3) the size of the error can be
reduced (but not to zero) by choosing a glucose distribution space much
below the total glucose distribution volume in the body. The error in
endogenous glucose production estimates in this experimental paradigm
is sufficiently large to necessitate variable tracer infusion to
minimize the error. By contrast, in the present dual-isotope paradigm,
the endogenous glucose production 1)
is in small error (see Ref. 9 and above),
2) when in error, is overestimated,
and 3) can be obtained using
one-compartment analysis and effective glucose distribution volume near
to the total glucose distribution volume; forcing a lower volume would force the introduction of an imbalance of structure and volume errors.
Furthermore, in the first of these two experimental paradigms, wherein
a negative hepatic glucose production problem has been identified, a
variable tracer infusion would be needed to minimize variation in the
tracer-to-total glucose ratio specifically, because it is total glucose
appearance that is estimated by modeling. By contrast, in the second,
and presently used, experimental paradigm, the endogenous (not total)
glucose production rate is estimated directly, and the variable tracer
infusion, when needed, would be to minimize the tracer to an endogenous
(not total) glucose ratio (9). This has implications for the error
estimates, for when total glucose appearance is estimated, it may be
associated with a rising C1 that,
according to Eqs. A6b and A6c, would magnify the error balance
er(t).
By contrast, when endogenous glucose appearance is estimated, it is
subject to a falling C1, which would diminish the error.
When estimates of Ra and glucose
disposal rate are not whole body estimates.
When exogenous glucose is administered intravenously, the estimates of
Ra are whole body estimates;
however, this is not the case when exogenous glucose is administered
via the oral or enteral route. Then
Ra, obtained by either one- or
multicompartment models, is for rates of entry into the systemic
glucose pool, which differs from the whole body glucose
Ra in a significant way. Thus the gut and liver have to be viewed as a single unit from which glucose appears, both endogenous and exogenous. With such models, the estimate
of systemic Ra is less than whole
body Ra by the rate of hepatic
sequestration of glucose that is derived directly from the gut. It
might be thought that dilution of tracer by unlabeled exogenous glucose
in the portal vein would interfere with making accurate
Ra estimates. However, provided
gut-derived glucose dilutes the tracer and tracee from the systemic
circulation equally, the principle of equivalent tracer supply is
upheld. It is worthy of note, however, that estimates of glucose
disposal rates, should they be made, will also not represent whole body
rates, as these will be underestimated by the rate of first-pass
hepatic glucose sequestration.
 |
ACKNOWLEDGEMENTS |
We thank the Ministry of Agriculture, Fisheries, and Food for
financial support and the Biotechnology and Biological Sciences Research Council for the provision of facilities.
 |
FOOTNOTES |
Address for reprint requests: G. Livesey, Dept. of Nutrition, Diet, and
Health, Institute of Food Research, Norwich Research Park, Colney,
Norwich NR4 7UA, UK.
Received 21 July 1997; accepted in final form 23 June 1998.
 |
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