Modeling intermittent digesta flow to calculate glucose uptake
capacity of the bovine small intestine
John P.
Cant,
Paul H.
Luimes,
Tom C.
Wright, and
Brian W.
McBride
Department of Animal and Poultry Science, University of
Guelph, Guelph, Ontario, Canada N1G 2W1
 |
ABSTRACT |
To test the hypothesis that the uptake
capacity of the bovine small intestine for glucose is upregulated to
match or slightly exceed glucose delivery, glucose was continuously
infused into the proximal duodenum of four cannulated holstein heifers.
Every 3 days, infusion rates were increased by an average of 34 mmol/h. A model of glucose disappearance from multiple boluses of intestinal digesta was used to estimate the transporter maximum velocity and
functional maximum uptake capacity for the entire small intestine from
average ileal glucose flows during the third day of each period.
Because of its intermittency, digesta flow remained independent of
simulated transit time. For each unit increase in glucose infusion rate, uptake capacity increased by only 0.55 units. Excess capacity for
glucose uptake was approximately twofold in forage-fed cattle and
declined to below delivery at infusions of >208 mmol/h added glucose,
approximately three times the normal load. Calculations for cattle,
sheep, and rats indicate that the glucose transport capacity of the
small intestine is typically underutilized because of a fraction of
time that transporters are not in contact with digesta.
glucose absorption; duodenal glucose infusion
 |
INTRODUCTION |
RUMINANT ANIMALS RELY ON gluconeogenesis from
endproducts of carbohydrate fermentation in the forestomach to produce
essentially all of the glucose used in metabolism. Although
quantitatively little free glucose enters the duodenum of adult
ruminants from dietary sources, starch that escapes ruminal
fermentation can be hydrolyzed by intestinal amylase and brush-border
disaccharidases to release its glucose monomers, which, for utilization
by the animal, must be transported out of the small intestine. Domestic cattle fed for high rates of growth or milk production may obtain 5-20% of their daily glucose flux by intestinal absorption (24). In many animals, the small intestine upregulates the number of glucose
transporters in the presence of additional luminal substrates (11).
This phenomenon has been demonstrated to occur in ruminants (27, 38,
45). For example, glucose infusion into the duodenum of adult sheep
increased the maximum velocity
(Vmax) of the
sodium-glucose cotransporter activity in brush-border membrane vesicles
to close to preruminant levels, a 40- to 80-fold change (38). It has been suggested that herbivores and omnivores modulate maximum uptake
capacity (MUC) of the small intestine for glucose to quantitatively meet or only slightly exceed the delivery of glucose (5, 14, 40).
Accordingly, in a review of farm animal intestine metabolism (7),
glucose MUC was defined as the highest disappearance of glucose from
beginning to end of a small intestine when postileal glucose loss is
negligible (an arbitrary 1% of starting or proximal concentration).
Cant et al. (7) considered MUC an emergent property of the positionally
dependent instantaneous
Vmax and the
Michaelis-Menten constant
(Km) for
glucose transport by intestinal epithelial cells, and they further
defined a functional MUC (fMUC) as that obtained during intermittent
digesta flow through the small intestine. It was demonstrated, using
data from two sheep infused with glucose into the abomasum (32), that
kinetic parameters of the uptake model, and, by numerical simulation,
fMUC, could be obtained by fit to observations of more-than-negligible
quantities of glucose appearing at the terminal ileum. MUCs for glucose
have not been estimated in cattle, so a modification of the Ørskov
et al. (32) experimental design was applied to four holstein heifers in
an attempt to exceed fMUC and thereby obtain its value. In so doing, we
have gathered evidence that fMUC for glucose is not upregulated in
cattle to maintain a slight excess capacity for glucose absorption beyond concurrent glucose delivery, as suggested for other species (14,
20, 40).
 |
METHODS |
Animals and animal care.
Four mature (45 ± 4 mo) holstein heifers (507 ± 16 kg) were
fitted with T-type cannulas 10-cm distal from the pylorus in the proximal duodenum and 10-cm proximal to the ileocecal junction in the
terminal ileum. Surgeries were completed 4 mo before the beginning of
this experiment. A maintenance ration containing 64% (dry
matter basis) timothy hay and 36% alfalfa hay was fed to
the animals in equal portions at 0600, 1200, 1800, and 2400 daily.
Feed and orts were weighed and sampled each day to
calculate dry matter and nutrient intakes. Crude protein, acid
detergent fiber, and neutral detergent fiber were determined by
near-infrared spectrometry (Agri-Food Laboratories, Guelph, ON).
Animal involvement in this experiment was approved by the
University of Guelph Animal Care Committee.
Treatments.
A solution of glucose containing 0.9% NaCl and 0.88 g/l cobalt-labeled
EDTA as an indigestible flow marker was prepared fresh daily (41) for continuous duodenal infusion with a peristaltic pump
(Gilson Minipulse 3, Villiers-le-Bel, France) at 5 l · day
1 · heifer
1.
Glucose delivery rate was increased simultaneously for all four heifers
by changing glucose concentration in the infusate at the beginning
(1200) of each of 14 consecutive 3-day periods. Glucose infusion began
at 0 g/h in period 1, was increased to
50 g/h in period 2, and was
incremented by 6.25 g/h with each period thereafter. There is a
reported time lag of 1-2 days in enhancement of intestinal glucose
transport because upregulation by substrate only occurs in developing
enterocytes that must migrate to the villus tip to be effective (13).
Three-day periods were chosen to give enough time for intestinal
adaptation to manifest itself before glucose infusion rate was
increased again.
To maintain fluid infusion rate constant across all treatments, it was
necessary to estimate, a priori, the highest level of glucose to be
infused. Functional MUC for glucose was exceeded in sheep by abomasal
infusion of >12.5 g/h glucose or ~0.98
g · h
1 · kg
0.75
(32). With the assumption that cattle would exhibit a similar upper
limit to glucose fMUC, it was decided at the outset to terminate the
experiment at 125 g/h glucose or 1.17 g · h
1 · kg
0.75.
The daily allotment of glucose at 125 g/h required 5 liters saline
solution for solubilization, so fluid infusion rate was set at 5 l · day
1 · heifer
1
for all periods.
Sample collection and analysis.
Glucose delivery rates were determined by monitoring infusate weight at
6-h intervals. Ileal digesta samples were collected every 6 h by
inserting a collection gate into the opened cannulas and waiting until
either 120 ml had been obtained or 45 min had elapsed. One hundred
milliliters were frozen for indigestible marker analysis, and 20 ml
were collected into 0.1 ml of 10 M NaOH to inactivate any residual
carbohydrase activity (26). These samples were centrifuged at 500 g, and the supernatant was removed and
kept at 4°C until analysis within 24 h for glucose by a glucose
oxidase spectrophotometric method (Sigma Chemical procedure no. 510, St. Louis, MO).
Samples frozen for marker analysis were thawed and spun at 34,500 g for 15 min. Supernatant was
collected and recentrifuged under the same conditions to ensure solid
matter was removed before cobalt determination by atomic absorption
spectroscopy (Varian Spectra 300, Varian Techtron, Mulgrave, Australia).
Calculations.
Glucose uptake (g/h) was calculated as
|
(1)
|
where
i = infusion rate (mmol/h),
[S]L = glucose
concentration in ileal digesta (mM), and F = ileal fluid flow rate
(l/h). Ileal fluid flow was determined by dividing the duodenal cobalt infusion rate by ileal fluid cobalt concentration.
The glucose uptake model of Cant et al. (7) considers the small
intestine a cylindrical tube through which digesta flow at a constant
linear velocity, albeit intermittently. The change in concentration of
glucose ([S]) with distance
x from the pylorus is a function of
saturable transport at the periphery of the cylinder and instantaneous
digesta flow rate according to
|
(2)
|
where
Vmax0 = maximum velocity of glucose transport at the proximal duodenum
(mmol · h
1 · cm
1),
k = linear slope of the decline in
Vmax along the
intestine (mmol · h
1 · cm
2),
D = digesta speed (cm/h),
A = cross-sectional area of the small intestine (cm2), and
Km = affinity
constant of the transport system (mM).
If digesta flow is continuous throughout the small intestine, glucose
concentration at any point x will be
defined by the integral of Eq. 2
between 0 and x. However, intestinal
contents move primarily with the migrating myoelectric complex that
recurs at 60- to 100-min intervals and lasts only 5-15 min (6,
34). This intermittency is simulated with a flow cycle of period
p (h) and duration
w (h). The glucose concentration
profile within a bolus becomes essentially the integral of
Eq. 2 between
x
Dw and
x, or, in terms of time, t,
between t
w and
t (see
APPENDIX).
Observations on day 3 of each period
were averaged by heifer and used to obtain model parameter estimates if
ileal glucose concentration was >1% of the calculated duodenal
concentration. The small intestine was assumed to be 4,000 cm in length
(39) with A equal to that of the
cannulas, i.e., 12.57 cm2.
Differences in observed F were presumed to be due to the number or size
of digesta boluses in the intestine at any one time (16), which was
accommodated by varying the parameter
w according to
|
(3)
|
Thus
linear velocity D and transit time of
each bolus were considered constant across treatments and heifers.
Transit time from beginning to end of the small intestine was measured
in one animal as 2.5 h from the time phenol red was dosed into the
duodenal cannula until first appearance of dye in ileal digesta. The
quotient of length (L) and transit
time yields D = 1,600 cm/h. A new
bolus of digesta appeared at the terminal ileum approximately every p = 1.2 h. Glucose uptake
Km was assigned a
value of 1.7 mM (7) and k was set to
Vmax0/L
so that Vmax at
the terminal ileum was 0. Finally, initial
Vmax was
calculated after integrating Eq. 2 to
yield
|
(4)
|
where
[S]0 = i/F.
Functional MUC was determined by first ascertaining the starting
concentration of glucose,
[S]0(fMUC), that would
result in an ileal concentration
[S]L = 0.01[S]0, to meet the
criterion of negligible postileal glucose loss at fMUC. Substituting
into Eq. 4 and rearranging
|
(5)
|
which,
given the constant parameter values discussed above, becomes
|
(6)
|
Aspects of intestinal physiology that are not accommodated by the model
include progressive and retrograde digesta flows and radial variation
in such. Longitudinal contractions of the intestine wall that
facilitate radial translocation of nutrients within digesta (8)
probably eliminate the potential for laminar flow to speed nutrients
out of the small intestine without access to the mucosa. Combined with
backward and forward movements of chyme, nonpropulsive motility causes
a mechanical averaging of nutrient contents within a bolus, which the
integral of Eq. 2 does mathematically.
The simplified representation of intestinal flow as an average slow
forward movement of discrete boluses should be adequate for our purpose
of simulating nutrient absorption from the entire small intestine.
There is no consideration of longitudinal variation in bolus size. In
other words, water absorption from the bolus as it travels distally is
not simulated. This affects the calculated starting concentration of
glucose {[S]0
and [S]0(fMUC)} but not the simulated uptake or MUC. A linear decline in
Vmax from
beginning to end of the small intestine is assumed and embodied in the
parameter k. The decline may in
reality be exponential, but our calculation of uptake requires only
that the area under the
Vmax curve (i.e.,
total Vmax) be
appropriate and the linear decline is a simpler representation of area.
The glucose uptake model (see
APPENDIX) was written in Advanced
Continuous Simulation Language (ACSL; Ref. 1), and 10 h were simulated
for each heifer × period from the initial conditions F,
Vmax0,
and [S]0(fMUC). Total
predicted glucose uptake between 5 and 10 h was expressed per hour to
provide the estimate of fMUC.
Statistical analysis.
Variances in i, [S]L
and F observations, and calculated glucose uptake values
were analyzed with a model that considered repeated measures over time
within each treatment period
|
(7)
|
where
Yi jk = dependent variable,
µ... = true grand mean,
Pi = period effect
(i = 1-14),
Hj = heifer effect
(j = 1-4), and
Tk = time effect
(k = 1-12). Period and heifer
effects were tested against the
PHij interaction term for significance.
Terms containing time as a factor were tested against the PHT
interaction,
eijk. Means were separated by a Duncan's multiple-range test.
Simulation results from the glucose uptake model were analyzed with the
simpler ANOVA model
|
(8)
|
 |
RESULTS AND DISCUSSION |
On average, the cattle consumed 9.8, 1.3, and 5.3 kg/day dry matter,
crude protein, and neutral detergent fiber, respectively. The diet
itself provided ~112% of the heifers' putative energy requirements
for maintenance (31), and upwards of 130% of requirements were met by
diet and glucose combined at the highest infusion rates. Glucose entry
into blood of these cattle during the first period, mostly from
gluconeogenesis, was calculated from intake observations to be 570 mmol/h (2), so the infusions potentially doubled glucose supply. The
treatment period was a statistically significant effector of dietary
nutrient intakes, but no large changes in supply were apparent; crude
protein intake tended to drop, whereas fiber intake rose with each
period (Fig. 1). One heifer was removed
from the experiment at the conclusion of period 9 due to inappetence and diarrhea. The entrance of
significant quantities of highly fermentable sugar into the large
intestine predisposes ruminants to diarrhea (42). Loose feces were
first observed in the remaining heifers during period
13 and began to diminish during period
14 at rates of glucose infusion into the proximal small
intestine of ~3 kg/day.

View larger version (15K):
[in this window]
[in a new window]
|
Fig. 1.
Average intakes of dry matter (solid line), crude protein (dotted
line), and neutral detergent fiber (dashed line) in 4 cattle infused
with glucose into the duodenum. All 4 heifers were infused
simultaneously with an identical rate of glucose infusion that was
increased at the beginning of each 3-day period to produce a range of
glucose deliveries from 0 to 700 mmol/h.
|
|
Three-day periods of glucose infusion were chosen to give enough time
for any upregulation of glucose transport activity that might occur to
manifest itself as a drop in ileal glucose flow by the end of the third
day. Across all treatment periods, the mean arrival of glucose at
the terminal ileum in millimoles per hour was significantly
different by sampling time, but it was hours
36, 48, and
60 that were higher than the 72-h
glucose flow, not hours 0-24
(Fig. 2). Time × period
(PTik) was a significant interaction
in the ANOVA in glucose loss, but, again, day
1 of sampling was only higher than day
3 in periods 7,
9, and
13. If glucose uptake capacity of the
small intestine is regulated to equal glucose delivery (14) and
upregulation takes 1-2 days to become complete (13), the expected
ileal glucose response to an increase in glucose infusion rate would be
as observed in period 11 (Fig.
3A). At
the onset of an increase in glucose infusion rate from 536 to 612 mmol/h, ileal glucose flow in heifer 3 increased immediately and after 12 h began to decline, reaching near 0 mmol/h by the third day. Two other heifers on the same treatment,
however, showed a slight rise in glucose outflow that was maintained
throughout the 3 days of infusion. Most of the variation in calculated
glucose outflow was due to changes in ileal glucose concentration; flow variation was an average of 41% of its mean within each period, whereas variation in glucose concentration was a much larger 89% of
the mean.

View larger version (13K):
[in this window]
[in a new window]
|
Fig. 2.
Average flows of glucose past ileal cannulas in 4 cattle simultaneously
infused with glucose into the duodenum. Each point represents the
average product of glucose concentration and digesta flow for all
animals across 14 sequentially increasing rates of glucose infusion
from 0 to 700 mmol/h (1 animal was removed from the experiment at 580 mmol/h glucose). Bars indicate SE.
|
|

View larger version (25K):
[in this window]
[in a new window]
|
Fig. 3.
Temporal patterns of glucose appearance at terminal ileum in cattle
infused with glucose into the duodenum. Glucose infusion rate was
increased every 3 days; A and
B show periods
10 and 11 and
periods 1 and
2, respectively. Thick solid lines
indicate glucose infusion rate, and points represent products of
glucose concentration and digesta flow measured at 6-h intervals. Solid
and dotted lines connect repeated observations on the same animal.
|
|
The lack of a temporal rise and fall in ileal glucose flow consistent
with a hypothesis of upregulation to match glucose uptake with
intestinal delivery may have been due to a large variation in glucose
infusion rate within periods. Standard errors of mean infusion rate in
each period ranged from 0 to 76.4 mmol/h with a mean of 23.2 mmol/h,
whereas the increment from one period to the next was intended to
be 34.7 mmol/h. Consequently, three consecutive days at a
given infusion rate were only obtained in 7 of 14 periods. In addition,
if there had been a slight excess in glucose uptake capacity over
delivery and that excess was more than the average 34.2 mmol/h
increment in glucose infusion rate, there would be no reason to expect
an increase in ileal glucose flow on the first day of any period.
However, the period 2 infusion rate
had a low standard error and a very large increment over the previous
period (275 mmol/h), and none of the heifers demonstrated an
adaptational response in small intestinal glucose outflow (Fig.
3B).
Complex carbohydrate digestion in the small intestine of these animals
was calculated with a dynamic model of the cow (2) to supply ~100
mmol/h glucose. The jump from 100 to 375 mmol/h by infusion in
period 2 was met with an increased
ileal outflow averaged over 3 days of only 4, 16, 4, and 23 mmol/h in
the four heifers, respectively (Table 1).
The small outflows suggest an almost threefold excess capacity for
glucose uptake in forage-fed cattle. Furthermore, as the
day 3 infusion rate increased with each experimental period, glucose uptake also increased, but it fell
below the line of unity (Fig.
4). Infusion rate was higher than the 95% confidence interval around the uptake mean; i.e., uptake
capacity was exceeded when delivery was more than 416, 582, and 270 mmol/h for heifers 1,
2, and
4, respectively.
Heifer 3 demonstrated a high capacity
for glucose uptake that was only significantly lower than infusion
rates of 582 and 651 mmol/h.
View this table:
[in this window]
[in a new window]
|
Table 1.
Observations of duodenal glucose infusion rate, ileal glucose
concentration, and ileal fluid flow rate in four cattle on the
third day of each of consecutive 3-day periods of infusion
|
|

View larger version (17K):
[in this window]
[in a new window]
|
Fig. 4.
Uptake and loss of glucose from the small intestines of
heifers 1-4
(A-D, respectively)
simultaneously infused with glucose into the duodenum. Glucose infusion
rate was increased by an average of 34 mmol/h every 3 days; solid lines
indicate changes in uptake determined from ileal digesta samples
collected every 6 h during the third day at each rate. Hatched area
represents glucose lost out of the small intestine unabsorbed.
|
|
Calculation of fMUC and parameters of glucose transport.
Our results indicate that, to overcome errors in measurement of glucose
flow at the ileum, an assay of unadapted glucose uptake capacity in
mature cattle would need a duodenal infusion near 600 mmol/h. Not
having had such prior information, we took the approach of measuring
ileal glucose at successively increasing infusion rates into the
duodenum. Uptake capacity could only be calculated when ileal glucose
exceeded 1% of duodenal concentration, but the criterion was met by
all infusion levels above 50 mmol/h. Results of the fMUC calculations
are presented for each heifer × period in Fig.
5 along with regression lines representing
fMUC and delivery as functions of glucose infusion rate. Although fMUC clearly increased with glucose infusion rate, the slope of the relationship (0.55 ± 0.08) was significantly less than
1.0. A general conclusion can be drawn, then, that uptake capacity of the bovine small intestine is not sufficiently upregulated to match
concomitant glucose delivery rate. In addition, the estimate of excess
capacity in forage-fed cattle can be refined by extrapolating the fMUC
line to 0 mmol/h infused glucose, where fMUC is 92.9 mmol/h over the
expected carbohydrate digestion rate of 100 mmol/h glucose, a twofold
excess.

View larger version (17K):
[in this window]
[in a new window]
|
Fig. 5.
Functional maximum uptake capacities (fMUC) of small intestines of 4 cattle simultaneously infused with glucose into the duodenum. Glucose
infusion rate was increased by an average of 34 mmol/h every 3 days;
each point represents estimated fMUC for each animal during the third
day at a given rate. Dotted line shows the linear regression of fMUC on
glucose infusion rate; y = 92.9 + 0.554 x, for which
r2 = 0.53. Solid
line has a slope of 1.0.
|
|
It is surprising that the small intestine was not at a maximally
attainable uptake capacity when fMUC was less than the glucose infusion
rate. For example, at an infusion rate of 614 mmol/h, fMUC was ~440
mmol/h, but when glucose was infused at 440 mmol/h, fMUC was ~360
mmol/h. Why did fMUC not increase to 440 mmol/h in the latter case? A
similar lag in upregulation has been demonstrated previously in sheep
and cattle (26, 32). Between 3 and 10 h after initiation of infusion of
111, 222, or 333 mmol/h glucose into the abomasum of 350-kg steers fed
alfalfa hay, Kreikemeier et al. (26) observed small intestinal uptakes
of 108, 189, and 237 mmol/h, respectively. The observations all fit the
criterion for estimation of uptake capacity. For each unit increase in
glucose infusion rate, uptake capacity increased by 0.56 units, in
agreement with the 0.55 unit increase we observed between 48 and 72 h
of infusion (Fig. 5). The similarity is curious and suggests that the
mechanism of upregulation was similar in both cases, despite the
expected increase in transporter number following the longer adaptation period.
Huntington (24) simulated the Kreikemeier et al. (26) results by
considering paracellular diffusion out of the intestinal lumen. Total
Vmax of the small
intestine for active transport of glucose was set at 175 mmol/h so that
increased uptake at higher infusion rates was predicted to be primarily
due to increases in paracellular transport rate. Diffusion accounted
for 6% of predicted glucose uptake at 111 mmol/h of glucose infusion
and 27% at 333 mmol/h (24).
There is argument as to the importance of paracellular transport for
glucose absorption from the small intestine. Ferraris et al. (14) and
Schwartz et al. (36) calculated uptake capacity by considering only
active transport and quantitatively accounted for absorption of the
daily carbohydrate intake of rats. Markers of the paracellular route,
such as L-mannose and
2-deoxyglucose, have been absorbed at <10% of the rate of
D-glucose absorption in rats and
cattle (25, 36). Increased
D-glucose supply did not
increase marker absorption in these experiments but actually reduced it
in some cases, indicating competition for a common transporter.
Schwartz et al. (36) suggested that the elevated intestinal glucose
uptake that occurs when apparently saturating glucose concentrations
are increased is due to diffusion through the unstirred layer between
villi. Only when intraluminal glucose concentration is high would there
be a drive for glucose to move the added distance to epithelial cells
further down the villus. In essence, the recruitment of more epithelium
is an increase in apparent
Vmax for active
glucose transport. Indeed, Levitt et al. (28) reported a doubling of
Vmax (and the
expected decrease in apparent
Km) when intact
rats were shaken at 250 rpm to reduce impact of the unstirred layer. An
increased apparent
Vmax at higher glucose concentrations could account for the similarity in slopes of
the uptake-delivery relationship observed here and by Kreikemeier et
al. (26). The intervillar diffusion explanation would also account for
the absence of a temporal rise and fall in glucose flow past the ileum
following each increment in glucose infusion rate. Thus, in our
modeling system, we chose to ignore the minor role of paracellular
diffusion and explain increased uptake capacity with a change in
Vmax.
Accommodation of intermittency of digesta flow.
The assumed linear decline in instantaneous
Vmax from
proximal to distal ends of the small intestine permitted calculation of
a total Vmax for
the entire length (4,000 cm) as 2,000 Vmax0. Linear and quadratic effects of period on total
Vmax were both statistically significant (P = 0.008 and 0.009, respectively), but linear regression against glucose
infusion rate only explained 14% of the variation in estimated total
Vmax (Fig.
6A).
Ileal fluid flow rate, however, accounted for 39% of the total
Vmax variance
(Fig. 6B). For each liter per hour
increase in flow, total
Vmax decreased by
449 mmol/h because fewer transporters are needed with increased flow
when that flow is due to a longer gush in from the stomach, as we have
assumed in our calculations (Eq. 3).
All other factors being constant, increased volume flow does not affect
rates of glucose disappearance at any point along the intestine
(Eq. 2); there is just a greater
proportion of the intestine in contact with digesta at all moments in
time and, therefore, a higher rate of solute uptake from the entire
tract. Effects of glucose infusion on digesta flow rates were similar to those observed for total
Vmax: linear and
quadratic increases with each period were significant
(P = 0.08 and 0.04, respectively), but
glucose infusion rate accounted for only 15% of flow variation (Fig.
6C). The synergy between flow rate
and total Vmax
can be captured by multiplying the two together or adjusting total
Vmax by the
proportion of time transporters are in contact with digesta. We propose
a functional total
Vmax
(ftVmax)
|
(9)
|
The
ftVmax increased
linearly and quadratically (P < 0.001) with period and was related to glucose infusion rate with a
correlation coefficient of 0.74 (Fig.
6D).

View larger version (24K):
[in this window]
[in a new window]
|
Fig. 6.
A-D
show relationships between estimated maximum velocity
(Vmax) for
glucose uptake from the entire small intestine of cattle, observed
digesta flow rates, and rates of glucose infusion into the duodenum. In
D,
ftVmax
is a total Vmax
corrected for flow according to Eq. 9.
|
|
Flow is governed by motility of the small intestine, which includes
both propulsive and nonpropulsive contractions. Paradigmatic of the
former is the migrating motor complex (MMC). In sheep, cattle, pigs,
and fasted rats, dogs, and humans, the MMC sweeps along the intestine
approximately once per hour, leaving a sustained quiescent phase in its
wake (43). Although regular occurrence of the MMC is replaced by rapid
irregular activity on consumption of a meal and for several hours
thereafter in nonruminants, propulsive contractions, which may only
propagate short distances along the intestine, still constitute about
half of the activity and occur every 5-40 s (9, 43). Gastric
emptying is much more rapid at this point, and the intense intestinal
activity accommodates the added flow. In the preruminant calf,
consumption of increased volumes of milk was accompanied by
augmentations in electrical spiking activity in the duodenum and number
of gushes of digesta from the stomach so that total volume flow was
elevated (16).
Fluctuations in gastric emptying are severely dampened in adult
ruminants by the relatively constant outflow from the rumen, so the MMC
continues in the fed state (6). Gregory et al. (19) reported that the
frequency of the MMC did not change when food intake of sheep was
restricted to 30% of ad libitum, even though abomasal outflow dropped
by 50%. Instead, the quiescent phase of the MMC was prolonged at the
expense of phase II irregular activity. It is at the transition from
phase II to phase III of the MMC that the majority of propulsion takes
place in sheep (6). The shorter duration of phase II probably reflected
smaller boluses entering from the abomasum, as observed by Girard and
Sissons (16).
Our formulation of the bolus flow problem, in which F = DAw/p
(Eq. 3), allows for three factors to
accommodate different observed digesta flow rates: the duration of
inflow or number of boluses w/p,
which was considered above, linear velocity
D (transit time), and cross-sectional
area A (distention). The intuition
that volume flow rate determines velocity of transit through the small
intestine is only valid when flow is continuous and at geometric
capacity of the vessel and when the vessel is rigid. However, there are numerous examples of braking mechanisms, opioid effects, secretory diarrhea, and so forth, in which increased gastric emptying is not
accompanied by a faster transit through the small intestine (3, 18, 21,
35). Although the patterns of intestinal motility that contribute to
variations in transit time have been documented (9, 37), the reasons
for a change in these patterns are not well understood. Nutrient
infusions into the ileum have slowed transit (22), but the
generalization that delayed transit improves nutrient absorption does
not always hold (29). The independent modulation of gastric emptying
and small intestinal transit time precludes use of
D as an accommodating variable for description of volume flow.
Downstream dye dilution from a rapid injection into the perfused
jejunal lumen of humans showed that as perfusate flow was increased
from 4 to 30 ml/min, the instantaneous volume of digesta in a 100-cm
segment increased curvilinearly from 250 to 500 ml (12). That volume
increase has been interpreted as a sign of intestinal distention (12,
15) but could also be the result of reduced deadspace in a partially
filled intestine, i.e., increased bolus size. If the intestine were
being stretched radially to accommodate greater flow rates in our
experiment, the
Vmax0 calculation (Eq. 4) would consider
A a variable dependent on flow (Eq. 3) and assign a constant value
to w. According to the distention explanation, the increase in fMUC as glucose delivery increased was
completely due to a change in transport
Vmax. The
ftVmax
(Eq. 9), however, was not affected
by the different assumption of flow accommodation.
Intermittent digesta flow and uptake capacity of the small intestine
for glucose.
Denoting a functional
Vmax highlights
the potential for a significant excess capacity to absorb nutrients
from the intestine as a consequence of it not being full of digesta at
all times. We have simulated intermittent flow in a standard model of
radial flux out of a tube, which continued the work of others (5, 10,
14, 33, 36, 40), to relate the kinetics of glucose uptake determined in
vitro with observed capacity in vivo. If our accounting for the
proportion of time spent in contact with digesta is appropriate, then
the observed flow rates of digesta should be the fraction
w/p
of the geometric capacity for flow, DA, the average volume of contents in
the small intestine should be that fraction of total volume, and the
uptake of glucose should be related to that fraction of total
Vmax.
Table 2 shows calculation of
ftVmax from a
total Vmax that
was measured in sheep by injecting 166 mM glucose solutions into ligated loops of small intestine and observing disappearance over a 1-h
period (45). Values for w and
p were used in a previous calculation
of fMUC for sheep (7) from the observations of Ørskov et al. (32).
In the current example, adjustment of the geometric flow capacity of a
typical sheep intestine of 6,125 ml/h by
w/p
yielded an F value of 835 ml/h, very close to the typical 800 ml/h for
sheep fed ad libitum (Table 2). The
ftVmax estimate
of 4.9 mmol/h is slightly less than the 6 mmol/h glucose entering the
small intestine. White et al. (45) measured total Vmax in six
different age groups of sheep, from 2 day old to adult, and our
estimates of
ftVmax from their
data, when regressed against glucose entry, yielded a slope of 0.58 mol/mol (r2 = 0.67). The slope is significantly different from 1.0 but not different
from 0.55 and 0.56, which were calculated from observations in cattle
(Fig. 5 and Ref. 26, respectively). The flow rate and uptake capacity
calculations (Table 2, Ref. 7) provide strong support for a model of
intermittent flow to describe nutrient absorption in ruminants.
In contrast to larger animals, duodenal or ileal fluid flow rates are
rarely measured in rats and gastric emptying is usually assessed
relative to a control treatment, not as an absolute rate. This makes
our calculations more difficult, but a first approximation of
w/p
can be obtained from the observation of Ferraris et al. (14). They
showed that 150 cm of rat intestine maintains a fairly constant fill
during the day of 1.7 g digesta. With a cross-sectional area of 0.035 cm2 (Table
3), the available volume is 5.25 ml and is
only 32% occupied. Gastric emptying of dry matter when food
consumption commences at night may be equal to the rate of ingestion,
which, at an average dry matter content of 40% (29), means that flow
into the small intestine may be 3-4 ml/h, greatly exceeding its
holding capacity. Distention must be the accommodating variable at such
times. Postfeeding, gastric emptying can be approximated as a
first-order process (46), which, over a 16-h period in adult rats,
produces an average flow of 1.0 ml/h (Table 3) or 38% of flow
capacity. There is evidence, therefore, that the proportion of time
that luminal transporters are in contact with digesta is significantly
less than 1.0 and a total
Vmax calculation
for the entire small intestine must be adjusted accordingly. Our
estimate of
ftVmax for rats consuming 42% glucose chow (14) was equal to the glucose intake (Table
3).
Diamond and co-workers (5, 14, 40, 44) have routinely measured
Vmax in everted
sleeves from different segments of intestine and then scaled up by
length or weight adjustments to the full organ. They have shown with
these calculations that uptake capacity is up- or downregulated to
slightly exceed supply of glucose to the intestine (5, 14, 40) or, in
cases where physiological load is high, to exactly match substrate
supply (44). If timing of substrate delivery is not accounted for, uptake capacity will be overestimated and will, at high loads, be
inadequate for uptake of all the glucose supplied, as we observed by
direct measurement in cattle. Regression analysis indicated a twofold
excess capacity, which declined to exactly match delivery at 208 mmol/h
added glucose (Fig. 5), ~3 times the normal load. Weiss et al. (44)
calculated a drop in glucose uptake capacity of the entire small
intestine of mice from 2.8 to 1.5 times sucrose intake as delivery
increased from 0.3 to 1.3 mmol/h with the demands of lactation. If a
discount for the time transporters were not in contact with digesta had
been utilized, no doubt the uptake capacity and delivery curves would
have intersected as in Fig. 5.
Although the ruminant animal, which does not rely on intestinal
absorption to obtain glucose, may be expected to spill unabsorbed glucose out of the small intestine, the upregulation of glucose transporters as substrate supplies or physiological loads increase cannot continue indefinitely in any animal, and there will be an upper
limit to achievable fMUC. Diamond and Karasov (11) listed costs of
transporter synthesis and maintenance, a fixed requirement for the
substrate, and its potential toxicity as factors determining the upper
limit for intestinal transport in general, but indicated that the
latter two do not apply particularly to glucose. More recently, Weiss
et al. (44) have included on that list the competition between
transporters and other proteins for membrane space in the
enterocyte. Intestinal growth could overcome such a limitation (7),
but, although compensatory growth is a common feature of nutritional
adaptation (17), it is obviously constrained, as is body size, to
maintain animal integrity. Any of these teleological explanations are
going to have to take into account the underutilized capacity for
transport that is expressed in the presentation of transporters on
villi not in contact with digesta. This particular fraction of total
uptake capacity may represent a safety factor for absorption of sudden
glucose loads if flow regulation by duration of inflow is common.
Alternatively, the underutilization is simply a cost of the plug-flow
design of the small intestine, wherein longitudinal distribution of
digestion and absorption at the circumference make for rapid and
efficient extraction of nutrients (23), although it begs the question of why flow is not continuous, as in capillary plug flow. Perhaps, because of meal feeding and bouts of fasting, the ability to handle or
expect continuous flow through the small intestine does not exist and
time becomes a major limiting factor in the absorption of nutrients.
 |
APPENDIX |
Equations describing flow variables and instantaneous rates of glucose
disappearance from multiple boluses of intestinal digesta were written
in ACSL (1), a program that solves differential equations numerically.
After each iteration through the following equations, time was
incremented by 0.005 h and a new state was predicted with a
fourth-order Runge-Kutta integration algorithm. State variables are
reservoir volume (R),
Vmax,
[S], and glucose uptake
(U) and were given initial values of
30 liters,
Vmax0, [S]0(fMUC), and 1.0 × 10
10 mmol/h,
respectively, for the first iteration through the model.
A reservoir of digesta at the proximal end of the small intestine
changes in volume according to
|
(A1a)
|
where
E and F' are digesta inflow and outflow (l/h) from the reservoir,
respectively. Inflow takes the form of a sine wave of amplitude
m about a mean flow of
E0 to approximate diurnal variation in the ruminant
|
(A1b)
|
where
T = time. Outflow from the reservoir
is pulsatile and is defined geometrically by intestine size as
|
(A2a)
|
where
z = 1 during the time interval
w, which begins every
p hours, and 0 for the remainder of
p (Fig.
7). Average digesta flow is then
|
(A2b)
|
Modulation
of F to equal a fluctuating E is brought about by one of three
mechanisms chosen by the user: either a change in
A, i.e., stretching the intestine so
that A = 1,000Ep/Dw,
changing the duration of inflow to the intestine to
w = 1,000Ep/DA,
or modifying linear velocity of digesta flow through the small
intestine to D = 1,000Ep/Aw.
If m = 0, A, w,
and D are constant throughout simulated time. Reservoir volume (R) is calculated by ACSL as the
integral of Eq. A1a.

View larger version (6K):
[in this window]
[in a new window]
|
Fig. 7.
Pulsing of z from 0 to 1 every
p hours and for
w hours of duration to control timing
of entrance of digesta into the small intestine from a reservoir.
|
|
Every p hours, at a time designated
starti, bolus
i of digesta begins to enter the small
intestine from the reservoir. ACSL performs the following integrations
for n boluses
|
(A3)
|
|
(A4)
|
|
(A5)
|
where
transit time tti = intestine length/D, and
ki = Vmax0/tti.
 |
ACKNOWLEDGEMENTS |
We thank those without whose help this project would have been
impossible: J. Bedford, D. Benschop, R. Berthiaume, G. Cottee, L. Fantin, W. Pearson, M. Perks, F. Qiao, and V. Volpe for help with
sample collection, laboratory work, and discussion, and P. DeVries and
J. Van Dusen for excellent care of the animals. We also extend thanks
to Bill Szkotnicki for keeping ACSL running on the mainframe.
 |
FOOTNOTES |
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Address for reprint requests and other correspondence: J. P. Cant,
Dept. of Animal and Poultry Science, Univ. of Guelph, Guelph, Ontario,
N1G 2W1 Canada (E-mail: jcant{at}aps.uoguelph.ca).
Received 12 November 1998; accepted in final form 8 March 1999.
 |
REFERENCES |
1.
Advanced Continuous Simulation Language.
ACSL Reference Manual. Concord, MA: Mitchell and Gauthier Associates, 1993.
2.
Baldwin, R. L.
Modeling Ruminant Digestion and Metabolism. London, UK: Chapman and Hall, 1995.
3.
Borody, T. J.,
E. M. M. Quigley,
S. F. Phillips,
M. Weinbeck,
R. L. Tucker,
A. Haddad,
and
A. R. Zinsmeister.
Effects of morphine and atropine on motility and transit in the human ileum.
Gastroenterology
89:
562-570,
1985[Medline].
4.
Brown, N. J.
Effect of nutrient infusions into jejunal and ileal Thiry-Vella loops on stomach-to-caecum transit (SCTT) in the rat (Abstract).
J. Physiol. (Lond.)
403:
43P,
1988.
5.
Buddington, R. K.,
J. W. Chen,
and
J. M. Diamond.
Dietary regulation of intestinal brush-border sugar and amino acid transport in carnivores.
Am. J. Physiol.
261 (Regulatory Integrative Comp. Physiol. 30):
R793-R801,
1991[Abstract/Free Full Text].
6.
Bueno, L.,
J. Fioramonti,
and
Y. Ruckebusch.
Rate of flow of digesta and electrical activity of the small intestine in dogs and sheep.
J. Physiol. (Lond.)
249:
69-85,
1975[Abstract].
7.
Cant, J. P.,
B. W. McBride,
and
W. J. Croom, Jr.
The regulation of intestinal metabolism and its impact on whole animal energetics.
J. Anim. Sci.
74:
2541-2553,
1996[Abstract/Free Full Text].
8.
Christensen, J.,
E. O. Macagno,
and
J. G. Melville.
Motility and flow in the small intestine.
J. Eng. Mech. Div.
104:
11-29,
1978.
9.
Cowles, V. E.,
and
S. K. Sarna.
Relation between small intestinal motor activity and transit in secretory diarrhea.
Am. J. Physiol.
259 (Gastrointest. Liver Physiol. 22):
G420-G429,
1990[Abstract/Free Full Text].
10.
Crane, R. K.
The physiology of the intestinal absorption of sugars.
In: Physiological Effects of Food Carbohydrates, edited by A. Jeanes,
and J. Hodge. Washington, DC: American Chemical Society, 1975, p. 2-19.
11.
Diamond, J. M.,
and
W. H. Karasov.
Adaptive regulation of intestinal nutrient transporters.
Proc. Natl. Acad. Sci. USA
84:
2242-2245,
1987[Abstract].
12.
Dillard, R. L.,
H. Eastman,
and
J. S. Fordtran.
Volume-flow relationship during the transport of fluid through the human small intestine.
Gastroenterology
49:
58-66,
1965.
13.
Ferraris, R. P.,
and
J. M. Diamond.
Crypt/villus site of substrate-dependent regulation of mouse intestinal glucose transporters.
Proc. Natl. Acad. Sci. USA
90:
5868-5872,
1993[Abstract].
14.
Ferraris, R. P.,
S. Yasharpour,
K. C. K. Lloyd,
R. Mirzayan,
and
J. M. Diamond.
Luminal glucose concentrations in the gut under normal conditions.
Am. J. Physiol.
259 (Gastrointest. Liver Physiol. 22):
G822-G837,
1990[Abstract/Free Full Text].
15.
Fine, K. D.,
C. A. Santa Ana,
J. L. Porter,
and
J. S. Fordtran.
Effect of changing intestinal flow rate on a measurement of intestinal permeability.
Gastroenterology
108:
983-989,
1995[Medline].
16.
Girard, C. L.,
and
J. W. Sissons.
The role of migrating myoelectric complexes in the regulation of digesta transport in the preruminant calf.
Can. J. Physiol. Pharmacol.
70:
1142-1147,
1992[Medline].
17.
Goss, R. J.
Theories of growth regulation.
In: Regulation of Organ and Tissue Growth, edited by R. J. Goss. New York: Academic, 1972, p. 1-11.
18.
Gregory, P. C.,
and
S. J. Miller.
Influence of duodenal digesta composition on abomasal outflow, motility and small intestinal transit time in sheep.
J. Physiol. (Lond.)
413:
415-431,
1989[Abstract].
19.
Gregory, P. C.,
S. J. Miller,
and
A. C. Brewer.
The relation between food intake and abomasal emptying and small intestinal transit time in sheep.
Br. J. Nutr.
53:
373-380,
1985[Medline].
20.
Hammond, K.,
and
J. Diamond.
Limits to dietary nutrient intake and intestinal nutrient uptake in lactating mice.
Physiol. Zool.
67:
282-303,
1994.
21.
Holgate, A. M.,
and
N. W. Read.
Relationship between small bowel transit time and absorption of a solid meal. Influence of metoclopramide, magnesium sulfate, and lactulose.
Dig. Dis. Sci.
28:
812-819,
1983[Medline].
22.
Holgate, A. M.,
and
N. W. Read.
Effect of ileal infusion of intralipid on gastrointestinal transit, ileal flow rate, and carbohydrate absorption in humans after ingestion of a liquid meal.
Gastroenterology
88:
1005-1011,
1985[Medline].
23.
Hume, I. D.
Optimization in design of the digestive system.
In: Principles of Animal Design, edited by E. R. Weibel,
C. R. Taylor,
and L. Bolis. Cambridge, UK: Cambridge University Press, 1998, p. 212-219.
24.
Huntington, G. B.
Starch utilization by ruminants: from basics to the bunk.
J. Anim. Sci.
75:
852-867,
1997[Abstract/Free Full Text].
25.
Krehbiel, C. R.,
R. A. Britton,
D. L. Harmon,
J. P. Peters,
R. A. Stock,
and
H. E. Grotjan.
Effects of varying levels of duodenal or midjejunal glucose and 2-deoxyglucose infusion on small intestinal disappearance and net portal glucose flux in steers.
J. Anim. Sci.
74:
693-700,
1996[Abstract/Free Full Text].
26.
Kreikemeier, K. K.,
D. L. Harmon,
R. T. Brandt, Jr.,
T. B. Avery,
and
D. E. Johnson.
Small intestinal starch digestion in steers: effect of various levels of abomasal glucose, corn starch and corn dextrin infusion on small intestinal disappearance and net glucose absorption.
J. Anim. Sci.
69:
328-338,
1991[Abstract/Free Full Text].
27.
Lescale-Matys, L.,
J. Dyer,
D. Scott,
T. C. Freeman,
E. M. Wright,
and
S. P. Shirazi-Beechey.
Regulation of the ovine intestinal Na+/glucose co-transporter (SGLT1) is dissociated from mRNA abundance.
Biochem. J.
291:
435-440,
1993[Medline].
28.
Levitt, M. D.,
J. K. Furne,
and
D. G. Levitt.
Shaking of the intact rat and intestinal angulation diminish the jejunal unstirred layer.
Gastroenterology
103:
1460-1466,
1992[Medline].
29.
Malagelada, J.-R.,
and
F. Azpiroz.
Determinants of gastric emptying and transit in the small intestine.
In: Handbook of Physiology. The Gastrointestinal System. Bethesda, MD: Am. Physiol. Soc., 1989, sect. 6, vol. I, pt. 2, chapt. 23, p. 909-937.
30.
Mathers, J. C.,
and
J.-M. Fotso Tagny.
Diurnal changes in large-bowel metabolism: short-chain fatty acids and transit time in rats fed on wheat bran.
Br. J. Nutr.
71:
209-222,
1994[Medline].
31.
National Research Council.
Nutrient Requirements of Beef Cattle. Washington, DC: National Academy Press, 1996.
32.
Ørskov, E. R.,
R. W. Mayes,
and
A. Penn.
The capacity for the removal of glucose from the small intestine by mature sheep.
Proc. Nutr. Soc.
30:
43A-44A,
1971.
33.
Pappenheimer, J. R.
Paracellular intestinal absorption of glucose, creatinine, and mannitol in normal animals: relation to body size.
Am. J. Physiol.
259 (Gastrointest. Liver Physiol. 22):
G290-G299,
1990[Abstract/Free Full Text].
34.
Rayner, V.,
and
G. Wenham.
Small intestinal motility and transit by electromyography and radiology in the fasted and fed pig.
J. Physiol. (Lond.)
379:
245-256,
1986[Abstract].
35.
Read, N. W.,
J. Cammack,
C. Edwards,
A. M. Holgate,
P. A. Cann,
and
C. Brown.
Is the transit time of a meal through the small intestine related to the rate at which it leaves the stomach?
Gut
23:
824-828,
1982[Abstract].
36.
Schwartz, R. M.,
J. K. Furne,
and
M. D. Levitt.
Paracellular intestinal transport of six-carbon sugars is negligible in the rat.
Gastroenterology
109:
1206-1213,
1995[Medline].
37.
Scott, L. D.,
and
R. W. Summers.
Correlation of contractions and transit in rat small intestine.
Am. J. Physiol.
230:
132-137,
1976[Medline].
38.
Shirazi-Beechey, S. P.,
B. A. Hirayama,
Y. Wang,
D. Scott,
M. W. Smith,
and
E. M. Wright.
Ontogenic development of lamb intestinal sodium-glucose co-transporter is regulated by diet.
J. Physiol. (Lond.)
437:
699-708,
1991[Abstract].
39.
Sisson, S.,
and
J. D. Grossman.
The Anatomy of the Domestic Animals. Philadelphia, PA: Saunders, 1953.
40.
Toloza, E. M.,
and
J. M. Diamond.
Ontogenic development of nutrient transporters in bullfrog intestine.
Am. J. Physiol.
258 (Gastrointest. Liver Physiol. 21):
G760-G769,
1990[Abstract/Free Full Text].
41.
Udén, P.,
P. E. Colucci,
and
P. J. VanSoest.
Investigation of chromium, cerium and cobalt as markers in digesta. Rate of passage studies.
J. Sci. Food Agric.
31:
625-632,
1980[Medline].
42.
Walker, D. M.,
and
G. J. Faichney.
Nutritional diarrhoea in the milk-fed lamb and its relation to the intake of sugar.
Br. J. Nutr.
18:
209-215,
1964.
43.
Weisbrodt, N. W.
Patterns of intestinal motility.
Annu. Rev. Physiol.
43:
21-31,
1981[Medline].
44.
Weiss, S. L.,
E. A. Lee,
and
J. Diamond.
Evolutionary matches of enzyme and transporter capacities to dietary substrate loads in the intestinal brush border.
Proc. Natl. Acad. Sci. USA
95:
2117-2121,
1998[Abstract/Free Full Text].
45.
White, R. G.,
V. J. Williams,
and
R. J. H. Morris.
Acute in vivo studies on glucose absorption from the small intestine of lambs, sheep and rats.
Br. J. Nutr.
25:
57-76,
1971[Medline].
46.
Yuasa, H.,
W. Numata,
S. Ozeki,
and
J. Watanabe.
Effect of dosing volume on gastrointestinal absorption in rats: analysis of the gastrointestinal disposition of L-glucose and estimation of in vivo intestinal membrane permeability.
J. Pharm. Sci.
84:
476-481,
1995[Medline].
Am J Physiol Gastroint Liver Physiol 276(6):G1442-G1451
0002-9513/99 $5.00
Copyright © 1999 the American Physiological Society