## 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

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 (*V*
_{max}) 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*V*
_{max} and the Michaelis-Menten constant (*K*
_{m}) 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
Equation 1where 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
Equation 2where
= maximum velocity of glucose transport at the proximal duodenum (mmol ⋅ h^{−1} ⋅ cm^{−1}),*k* = linear slope of the decline in*V*
_{max} along the intestine (mmol ⋅ h^{−1} ⋅ cm^{−2}),*D* = digesta speed (cm/h),*A* = cross-sectional area of the small intestine (cm^{2}), and*K*
_{m} = 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
).

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 cm^{2}. 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
Equation 3Thus 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*K*
_{m} was assigned a value of 1.7 mM (7) and *k* was set to
/*L*so that *V*
_{max} at the terminal ileum was 0. Finally, initial*V*
_{max} was calculated after integrating *Eq. 2
* to yield
Equation 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
Equation 5which, given the constant parameter values discussed above, becomes
Equation 6Aspects 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*V*
_{max} 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*V*
_{max} curve (i.e., total *V*
_{max}) be appropriate and the linear decline is a simpler representation of area.

The glucose uptake model (see
) was written in Advanced Continuous Simulation Language (ACSL; Ref. 1), and 10 h were simulated for each heifer × period from the initial conditions F,
, 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
Equation 7where Y_{i jk} = dependent variable, μ_{...} = true grand mean, P_{i} = period effect (*i* = 1–14), H_{j} = heifer effect (*j* = 1–4), and T_{k} = time effect (*k* = 1–12). Period and heifer effects were tested against the PH_{ij} interaction term for significance. Terms containing time as a factor were tested against the PHT interaction,*e _{ijk}
*. Means were separated by a Duncan’s multiple-range test.

Simulation results from the glucose uptake model were analyzed with the simpler ANOVA model Equation 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.

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 (PT_{ik}) 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.3
*A*). 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.

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.3
*B*).

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.

#### 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.

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*V*
_{max} 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 ofd-glucose absorption in rats and cattle (25, 36). Increasedd-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*V*
_{max} for active glucose transport. Indeed, Levitt et al. (28) reported a doubling of*V*
_{max} (and the expected decrease in apparent*K*
_{m}) when intact rats were shaken at 250 rpm to reduce impact of the unstirred layer. An increased apparent*V*
_{max} 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*V*
_{max}.

#### Accommodation of intermittency of digesta flow.

The assumed linear decline in instantaneous*V*
_{max} from proximal to distal ends of the small intestine permitted calculation of a total *V*
_{max} for the entire length (4,000 cm) as 2,000
. Linear and quadratic effects of period on total*V*
_{max} 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*V*
_{max} (Fig.6
*A*). Ileal fluid flow rate, however, accounted for 39% of the total*V*
_{max} variance (Fig. 6
*B*). For each liter per hour increase in flow, total*V*
_{max} 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*V*
_{max}: 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.6
*C*). The synergy between flow rate and total *V*
_{max}can be captured by multiplying the two together or adjusting total*V*
_{max} by the proportion of time transporters are in contact with digesta. We propose a functional total*V*
_{max}(ft*V*
_{max})
Equation 9The ft*V*
_{max} increased linearly and quadratically (*P* < 0.001) with period and was related to glucose infusion rate with a correlation coefficient of 0.74 (Fig.6
*D*).

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
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*V*
_{max}. The ft*V*
_{max}(*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*V*
_{max} 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*V*
_{max}.

Table 2 shows calculation of ft*V*
_{max} from a total *V*
_{max} 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 ft*V*
_{max} 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*V*
_{max} in six different age groups of sheep, from 2 day old to adult, and our estimates of ft*V*
_{max} from their data, when regressed against glucose entry, yielded a slope of 0.58 mol/mol (*r*
^{2} = 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 cm^{2} (Table3), 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*V*
_{max} calculation for the entire small intestine must be adjusted accordingly. Our estimate of ft*V*
_{max} for rats consuming 42% glucose chow (14) was equal to the glucose intake (Table3).

Diamond and co-workers (5, 14, 40, 44) have routinely measured*V*
_{max} 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.

## Acknowledgments

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.

## 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),*V*
_{max}, [S], and glucose uptake (*U*) and were given initial values of 30 liters,
, [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
Equation A1awhere 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 E_{0} to approximate diurnal variation in the ruminant
Equation A1b where*T* = time. Outflow from the reservoir is pulsatile and is defined geometrically by intestine size as
Equation 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
Equation 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* = 1,000E*p*/*Dw*, changing the duration of inflow to the intestine to*w* = 1,000E*p*/*DA*, or modifying linear velocity of digesta flow through the small intestine to *D* = 1,000E*p*/*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. EA1a
*.

Every *p* hours, at a time designated start_{i}, bolus*i* of digesta begins to enter the small intestine from the reservoir. ACSL performs the following integrations for *n* boluses
Equation A3
Equation A4
Equation A5where transit time *tt _{i}
*= intestine length/

*D*, and

*k*= /

_{i}*tt*.

_{i}## Footnotes

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).

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.

- Copyright © 1999 the American Physiological Society