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Blood flow to the rabbit pancreas with special reference to the islets of langerhans
GASTROENTEROLOGY
79:408-473,1989
Blood Flow to the Rabbit Pancreas with Special Reference to the Islets of Gngerhans NATHAN LIFSON, KEITH G. KRAMLINGER, MAYRAND, and E. JANE LENDER Department Minnesota
of Physiology,
University
of Minnesota
Nonradioactive microspheres of various sizes (mean batch diameters ranging from 6 pm to 26 pm) were administered to unfasted rabbits under sodium pentobarbital anesthesia by a brief injection into the left ventricle. Flow rate per bead was determined by the reference organ method. After prompt death of the animal, the spheres were located and counted microscopically (islet vs. nonislet) in fixed, stained, and cleared portions of the pancreas. According to an analysis of the distribution of spheres as a function of bead diameter, U-23% of the total pancreatic blood flow went directly to the islets and 77-89% to the “acini” (nonislet tissues). After retrograde postmortem injection of spheres 6 pm, 9 pm and 11 pm in diameter, practically none reached the islets, whereas after orthograde postmortem injection, they did so in the same proportions as in vivo. These results, supplemented by certain control experiments, support the view that all, or nearly all, efferent islet blood jlow goes to the acinar capillaries before leaving the organ. We conclude that the arterial supplies to the rabbit exocrine and endocrine pancreas are in parallel, with most of the flow going to the exocrine portion. However, the jIow to the islets is large enough to permit significant local actions of the islet hormones on the exocrine pancreas, in confirmation of the existence of an insuloacinar portal system. One finds in the literature fundamental disagreements concerning the relationship between the Received August X,1979. Accepted April 8,198O. Address requests for reprints to: Nathan Lifson, Department of Physiology, University of Minnesota, 6255 Millard Hall, 435 Delaware St. SE, Minneapolis, Minnesota 55455. This work was supported in part by U.S. Public Health Service National Institutes of Health Grants AM 19209 and AM 25897. We thank Korey Knutson, Daniel P. Fristoe, and Julie K. Drier for their technical assistance. 0 1980 by the American Gastroenterological Association 0016-5085/80/09046f3-0$02.25
Medical
ROBERT
School,
R.
Minneapolis,
blood supplies of the islets and acini in the mammalian pancreas. For purposes of discussion, the realistically possible topography of the circulation to a pancreatic lobule may be simplified as shown in Figure la, excluding A-V shunts for which there is no evidence. At one extreme is the view that the two supplies are in parallel and practically independent,‘,’ as in Figure lb. At the other extreme is the view that virtually all the blood of the pancreas first goes to the islets and then to the acini. That is to say, except in parts of the gland without islets, the islet and acinar supplies are in series,3-B as in Figure lc, an arrangement constituting an insuloacinar portal system which provides for a local action of the insular hormones at high concentrations on the acini. Intermediate views by otherP add a significant acinar flow to an insuloacinar flow, as in Figure Id, even in parts of the gland with islets. Still another view is that the acinar and islet flows are in parallel, but with communications, as in Figure la.8 Species differences do exist? but they are not responsible for the gross discrepancies among the various proposed arrangements. So far as we are aware, flow from acini to islets has not been directly observed, although its occurrence has been speculated upon in disturbances of the circulation? Thus, at present two fundamental questions concerning the pancreatic circulation are as follows: (a) Of the pancreatic blood flow, how much “normally” goes directly to the islets vs. directly to the acini? And (b) of the fraction going directly to the islets, how much then goes to the acini (vs. bypassing the acini and going directly to veins)? The living acinar and islet circulations were observed microscopically more than a century ago,l’ and a number of times since up to the present.” Red cell velocities in acinar capillaries have been measured,” but otherwise there does not seem to be any quantitation of the flows in question.
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(a)
serw case
P-@-1
33 (b)
Methods
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467
islet capillaries and none in the islets. On the other hand, if the acinar and islet circulations are independent (as in the parallel arrangement, Figure lb), the trapped beads should be distributed between nonislet and islet tissues more or less as they are found to be when entering the organ via the arteries. The conclusions reached will amount to adding the actual values for perfusion to the arrangement of the circulation in Figure Id.
-
Porollel case
BLOOD FLOW
Case
Figure 1. Diagrams of proposed arrangements of pancreatic circulation. a. Realistically possible topography of the circulation of a pancreatic lobule. b. Parallel limiting case. Acinar and islet circulations are completely independent. c. Series limiting case. All direct flow is first to islets and then to acinar capillaries via an insuloacinar portal system. d. Intermediate case. Acinar and islet flows are in parallel, with all efferent islet flow going to acinar capillaries as in c.
It appeared to us that answers to these questions might be obtained by an approach we had used to investigate the intraorgan distribution of blood flow to the small intestine.‘” This approach uses nonradioactive microspheres localized and counted in the intestinal tissues by microscopy. Two different types of experiments will be described, each directed at answering one of the two questions posed, with both types depending on distinguishing between spheres trapped in islets and spheres trapped in nonislet tissue (“acini”). To obtain data bearing on the first question, the microspheres were administered in vivo into the heart, as is conventionally done. To obtain data bearing on the second question, the spheres were administered postmortem by perfusion in the retrograde direction, based on the following rationale. Assume that the spheres are of such a diameter that they would reach the acinar capillaries and be trapped in them if reached, and also assume that the same holds for the islet vessels. Then, to take limiting cases, if the blood supply of the islets is in series with that of the acini (insuloacinar portal system, Figure lc),all the spheres will be trapped in the non-
In Vivo Administration
of Microspheres
Unfasted New Zealand white rabbits weighing about 2 kg were used. The animals were anesthetized by intravenous injection of a combination of 30 mg/kg sodium pentobarbital (Nembutal) and 5 mg of diazepam (Valium). “Carbonized” nonradioactive polystyrene microspheres (Nuclear Products Division, 3M Company, St. Paul, Minn.) were suspended in 0.9% NaCl containing 0.005% Tween 20 (polyoxyethylene sorbitan monolaurate). The suspension was held in an ultrasonic sonicator (ColeParmer, model 8845-3) and shaken by hand before injection into the left ventricle of the heart through a catheter (PE 60) inserted via the left common carotid artery. The arterial blood pressure was monitored by pressure transducer and recorder to ascertain proper positioning of the catheter. Duration of the injection was about 5 set, and the volume injected was 1 ml/kg. Batches of five mean diameters of microspheres were used: “6 pm” (6.1 f 2.0 (SD) pm), “9 pm” (8.9 f 1.1 (SD) am), “11 pm” (10.9 f 1.0 (SD) pm), “16 pm” (16.0 f 1.8 (SD) pm), and “26 pm” (25.8 f 3.4 (SD) w). (The results with “16 pm” spheres will include one experiment with “15 pm” spheres.) The quotation marks will be used to denote a batch of spheres with a given rounded off mean diameter. Cumulative percentage frequency distributions of diameters are shown in Figure 2. The approximate numbers of spheres administered per kilogram of animal were as follows: for “6 pm” spheres, 1Oe;for “9 pm” spheres, 2 X 107;for “11 pm” spheres, 107; for “15 pm” spheres, 7-9 x l@, and for “26 pm” spheres, 106.
A value for the rate of blood flow per microsphere
Diameter
was
in p.m
Figure 2. Cumulative percentage frequency distributions ameters of administered microspheres.
of di-
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LIFSON ET AL.
obtained by the reference organ methodI by means of a blood sample withdrawn by pump from the lower abdominal aorta at a known constant rate via a cannula inserted into the femoral artery. The blood sample was immediately examined under the microscope for clumping of spheres, and essentially none was seen. The total number of spheres in the blood sample was obtained by counting the number of spheres in aliquots placed on a slide and covered with a glass cover slip. The syringe is in effect an organ of known flow which completely traps the spheres and which is assumed to receive blood identical with respect to bead content to the blood received by the region under investigation. Then the rate of blood flow per sphere becomes the rate of withdrawal divided by the number of spheres in the total withdrawn blood sample. After the microsphere injection and femoral arterial blood collection, the rabbits were sacrificed by intraventricular injection of a saturated KC1 solution. Visualizing both the islets and the trapped spheres was accomplished by sequential in situ arterial perfusion of the pancreas of the sacrificed rabbit with heparinized isotonic saline, formalin, hematoxylin, and water, followed by removal of the tissue for dehydration in ethanol and clearing in methyl salicylate, as described and illustrated elsewhere.” A piece of pancreas about 2 cm* in area was cut from a location within the loop of the duodenum approximately at the level of the main pancreatic duct. Under a dissecting microscope, most of the mesentery and fat was teased away from the piece which was then moderately stretched and made fairly flat so that there were relatively few overlapping lobules. The cleared piece was examined under a dissecting and/or a standard compound microscope to make the following measurements: its area, its thickness in a number of locations, the number of islets in it, the diameter of its islets, the number of islet spheres, and the total number of spheres. Mean single islet blood flow (sif) was calculated from the product of the average number of spheres per islet (which ranged from 0.17 to 0.85) and the reference organ value of flow per sphere. The number of islets per gram of pancreas averaged 2.45 f 0.88 (SD) x 104, and the volume per islet averaged 0.80 nl, from which the total islet volume averaged 1.5% of the organ. Only rarely were islets with diameters less than 50 pm seen, and the smallest were 40 pm in diameter. From the above types of measurements, absolute values were calculated for the arterial perfusion of the organ, its distribution between islets and acini (strictly speaking, nonislet tissue), and the intensity of perfusion of the two types of tissue. Comparisons were made between the microscopic measurements of the volume of the pieces of pancreas carried through the staining and clearing procedures and the volume of fresh untreated pancreas. It was found that the mean volumes calculated in these two ways for a series of 12 pieces were practically identical so that the microscopic determination caused no systematic error. However, the two types of values for the volumes of the individual pieces (taken as equal to weight) differed on the average by 19%. Hence, one can expect considerable rabbit-to-rabbit variability among values expressed per gram of pancreas from this source alone.
GASTROENTEROLOGY
Vol. 79, No. 3
Inherent statistical variability also contributed to the observed rabbit-to-rabbit variability of the results. This contribution was greatest for the values of single islet flow, since only on the order of 70-100 islet spheres were usually counted to provide the values for spheres per islet. However, the observed rabbit-to-rabbit variability was large enough for the inherent statistical variability due to sphere counts to be negligible compared with other sources of variability.
Postmortem Microspheres
Administration
of the
Retrograde postmortem administration of spheres at a dose approximately 10% of the in vivo dose was via a cannula in the portal vein, preceded by a small volume of heparinized isotonic NaCl and followed by 100 ml of the saline. The injection pressures were under 100 cm H,O. The staining procedure was carried out in the usual orthograde direction. Experiments were also done in which all solutions, including the microsphere injectate, were administered postmortem in the orthograde direction. In some retrograde microsphere experiments the procedure was varied in that formalin fixation was retrograde instead of orthograde; in others the perfusate outflows were collected for determination of the number of spheres in them. The distribution of spheres in the pieces of pancreas which received the spheres by postmortem injection, either retrograde or orthograde, was measured somewhat differently than in the above in vivo experiments. Instead of carefully focusing to categorize candidate islet spheres as actual islet spheres, the following less time consuming procedure was used. The total area of a region of the essentially flat piece of pancreas was divided into that seen within the maximum diameters of the islets (“islet area”) and that outside these diameters (“nonislet area”). The spheres within these two areas were counted to give values for the fraction of the spheres in the whole thickness of the region within the islet area, designated as “islet core spheres.” Another measurement made was that of the number of islet spheres seen when the microscope was focused on the equatorial plane of the islets and kept there. The islet spheres seen with this procedure were designated as “equatorial islet spheres.” For comparison, similar measurements were made on tissues from the in vivo experiments. The measure of variability of a mean will be its SE unless otherwise indicated. Statistical significance between mean values was calculated by use of the Student t-test.
Results for Single Islet Flow @if) and Pancreatic Organ Perfusion as Calculated from Spheres of Different Mean Diameters Administered In Vivo Values
Figure 3 is a plot of the values of sif as a function
of sphere
diameter.
Similar
mean
values
were
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I 0 0
I
I
1
/
5
IQ
I5
20
, _I51
25
30
00’
0
= 3
’ 5
469
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I
/
/
I
IO
I5
20
25
‘Diameter” of Spheres (Micra)
“Diameter’ of Spheres (Micra) Figure 3. Calculated values for single islet blood flow (sif) as obtained from the administration of microspheres of different batch mean diameters. The measure of variability is the SE. The number of experiments is in parentheses. A value of sif = 0 is plotted at 4 pm because when “6qm” spheres were administered, no injectate spheres less than 4.5 pm were found in the is-
OF PANCREATIC
Figure 4. Calculated values for pancreatic perfusion as obtained from the administration of microspheres of different batch mean diameters. Measure of variability is the SE. The number of experiments is in parentheses. A zero value for pancreatic flow is plotted at 3 pm because when ‘%-pm” spheres were administered, no injectate spheres less than 3.5 pm were found in the tissue.
lets.
obtained with “11 pm” and “16 pm” spheres, 7.16nl and 6.74 nl/min, respectively. The mean value obtained with “9 pm” spheres was about 15% less (5.94 nl/min), but it was not significantly different from However, the value with the larger beads (P > 0.15). a significantly lower flow of about 70% less (2.16nl/ min) was calculated from “6 pm” spheres, the smallest injected. The sif for the largest spheres injected (“26pm”) was zero, i.e., virtually none of these was found in the islets. The value in Figure 3 at 4 pm is also placed at zero, because although approximately 30% of the administered “6 pm spheres were I 4.5 pm in diameter, none of these was found in the islets. The values calculated for sif shauld not be the same for all batches of spheres: Batches of spheres with sufficiently large or sufficiently small “diameters” should both give low values, the large ones because some of the spheres in the batch would not reach the islets, and the small ones because some of the spheres in the batch might shunt through the islets. Batches of intermediate “diameters” would also give low values to the extent that they were subject to both pre-islet trapping and islet shunting. The best estimates for sif, about 7 nl/min, are apparently obtained from “11 pm” and “16 pm” spheres. The question of estimating the true sif from the values in Figure 3 will be considered in the Discussion. Calculated values for pancreatic organ perfusion as a function of mean sphere injectate diameter are plotted in Figure 4. Mean values rise from 0.56 f 0.11 ml * min-’ *g-’ for “6 /.un” spheres to 1.09 f 0.10 ml - min-’ *g-’ for 22 experiments with spheres “9 pm” and larger. Apparently the fractional trapping of “16 pm” and “11 pm,” and even “9 pm” spheres, but not “6 pm”
spheres, was large enough to give values for organ perfusion like those for “26 pm” spheres which do not shunt through the organ.18”’ A value of zero perfusion was assigned to spheres 3 pm in diameter because although more than 10% of the administered “6 pm” spheres were ~3.5 pm in diameter, virtually none was seen in the pancreatic lobules. Results of Postmortem Microspheres
Administration
of
Results of the postmortem administration of “11 pm” spheres are shown in Figure 5. It is seen that when in this type of experiment the spheres were administered in the retrograde direction, only 3-5% 30,
0
OKI 0 12
i
3
:
4
!
5
i
6
I
: s : : ’ 7! 8 9 IQ II 12
% of Area of Piece Occupied
by Islets
Figure 5. Relationship in experiments with “11-pm” spheres between (a) the percentage of pancreatic “islet core spheres,” i.e., those in the whole tissue thickness within the circumference of islets, and (b) the percentage of area occupied by the islets. The line in the figure gives the relationship for random distribution of the spheres in the islets and nonislet portions of the tissue. Ortho = orthograde administration of microspheres. Retro = retrograde administration of microspheres.
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of the tissue spheres were “islet core spheres.” Essentially none of these was an “equatorial islet sphere” (data not shown). Since 5.5-8.0%of the tissue area was within the islet circumference, there were even fewer spheres in the islet cores than would have been found from a random distribution of spheres in islet and nonislet tissue. The plotted points fall below the line drawn in Figure 5 for such random distribution. Apparently few if any of the “11 pm” spheres had reached the islets, consistent with a series portal arrangement of practically all insular flow. The location of the spheres after their retrograde injection was in marked contrast to the findings in the in vivo experiments, in which 15-27% of the spheres were “islet core spheres” when the area containing these spheres made up only 5-8% of the total area, reflecting the greater concentration of spheres in the islets. Actually, nearly all these core spheres were in the islets, since the “11-pm” islet spheres averaged about 20% of the organ spheres. “Equatorial islet spheres” amounted to 8-14% of the total (data not shown). The postmortem orthograde sphere injections described in Methods were done to test for whether a change in the vasculature during the postmortem bead injection might have been responsible for the differences between in vivo and postmortem retrograde microsphere distributions. The results from the postmortem orthograde bead injections were like those from in vivo administration of the spheres (Figure 5).Hence, no evidence was obtained that the state of the vasculature was significantly different in the postmortem experiments with respect to trapping of spheres from that when the spheres were injected in vivo. The findings from use of “9 pm” spheres were similar to those from use of “11-pm” spheres (data not shown), as were the results for the “6-pm” spheres, except that with these smaller spheres the percentage of islet spheres (either “core” or “equatorial”) was less than for the larger spheres. This latter relationship is consistent with the values in Figures 3 and 4 which indicate a smaller fractional trapping of “6-pm” spheres by islet capillaries than acinar capillaries. The results were also similar whether the formalin fixation was by orthograde or retrograde administration before the staining and washing steps with the latter two always being orthograde. Moreover, only small percentages of the administered spheres were recovered from the fluids leaving the organ via the arteries during the retrograde injections or via the veins during the subsequent staining and washing steps. For example, in “11-pm” experiments of this type, 3 + 1% (n = 3) of the adminis-
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tered spheres were recovered in the arterial outflow and 7 + 2.4% (n = 7)from the orthograde venous outflow during the staining and washing perfusions. It is to be noted that the pancreas formed only a small portion of the weight of tissues perfused.
Discussion Correct values for sif depend in the first instance on correct counts for spheres per islet and correct reference blood values for flow per sphere. Aside from inherent statistical effects, to which reference has been made in Methods, incorrect values for spheres trapped per islet would arise if there were unstained (unseen) islets and if the value for spheres per islet were different in these islets from those in the stained (seen) islets. They could also arise if spheres were incorrectly assigned to seen islets. We do not believe that errors of this sort were large because of the appearance of the stained tissues and because the islet numbers and volumes are like those in the literature. There is good evidence that the value for flow per sphere obtained from the abdominal aorta by the reference organ technique should be a satisfactory one.‘e*1e-20 Even given correctly counted spheres per islet and the correct flow per sphere, sizable systematic errors in the values for sif could have been produced if the following assumptions were seriously invalid: (a) that all spheres in the blood destined for the islets reached the islets; (b) that only such spheres reached the islets; and (c) all the spheres reaching the islets were trapped in them. The fraction of spheres in the arterial blood flow trapped in a given vessel bed should be chiefly contingent on two frequency distributions: The first is the frequency distribution of the diameters of the blood spheres. This distribution is known from measurement (Figure 2). The second is the frequency distribution of the probability of a sphere entering the vessels. The microsphere method assumes that this probability is proportional to flow and hence related to a higher power of the diameter (the fourth power for streamline flow). The reported coefficient of variation of the distribution of geometric diameters of pre-islet arterioles and islet capillaries is about 0.25,2*~22and the corresponding coefficient of variation of the frequency distribution of flow as a function of diameter should be only moderately larger. Given this information about the two frequency distributions in question, the results in Figure 3 permit inferences to be drawn with some confidence from rather simple semiquantitative considerations. Thus, that the mean “6 pm” sif is only about one-third as great as the mean “9 pm” sif places the trapping diameters of the islet vessels car-
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1980
rying most of the flow between 6 pm and 9 pm. In this case all but a small fraction of the “11 pm” and an even larger fraction of the “16-pm” spheres reaching the islets would be trapped in them. Further, since both “11-pm” and “16-pm” spheres yielded similar values for sif, the pre-islet vessels did not distinguish demonstrably within the variability of the observations between these two injectate diameters. In view of the size distributions of these spheres (Figure 2), the diameters of the pre-islet vessels carrying most of the flow to the islets are thus placed at 16 pm and larger; but they are less than about 22 pm since “26-pm” spheres did not reach the islets. Accordingly, it appears that only a small fraction of either the “11-pm” or “16-pm” spheres in the blood destined for the islets was trapped in pre-islet vessels; and, having arrived in islets, only a small fraction failed to be trapped in them and to this extent supported the validity of assumptions (a) and (c) for these spheres. The validity of assumptions (a) and (b) also requires that the spheres be distributed in pancreatic arterial blood in proportion to flow until the blood enters the afferent arterioles of the islets. Effects dissociating volume and sphere flow (such as nonrandom radial distribution of spheres in the blood by inadequate mixing, axial streaming, and plasma skimming; and the flow velocity effect of Fung’“) are undoubtedly occurring to some degree in the microcirculation. We do not know the direction and magnitude of systematic errors in sif produced by these effects. A source of invalidity of the assumptions in these particular experiments which is not present in the usual microsphere measurements of blood flow is the staining procedure. One cannot be sure that the postmortem flows of perfusion fluids in the procedure have not moved microspheres. One reason for believing that such an effect has not been large is that the postmortem perfusion of intestinal wall with silicone latex did not cause detectable differences in the distribution of microspheres in the intestinal tissue layers.13 Another reason is that when the fluid draining from the portal vein during the staining procedure was collected and examined for its content of microspheres, it was found that the total of these spheres were a minor percentage of those remaining in the tissues. If invalidity of the assumptions caused a gross overestimate of sif, say by 50%, the true value would be 2/3 X 7.0, or about 4.6 nl/min. Our subsequent calculations involving sif will be reported as the range obtained by using what seem to us conservatively wide limiting values of 5 and 10 nl/min, bracketing the “best” mean values of 6.74-7.12 nl/min from Figure 3. Validity of the mean value for pancreatic organ
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perfusion (1.09 -+ 0.10 ml - min-’ 9g-‘) as estimated by the “9 pm” and larger spheres is subject to fewer sources of uncertainty than is the estimate of sif which depends on intraorgan factors. The only requirements are that the values of flow per sphere and spheres trapped per gram of pancreas be correct. The above value is more than double the flows of close to 0.40 ml - min-’ . g-’ reported previously for the rabbit pancreas.“.” Part of the disagreement may be due to the more nearly complete removal of fat and mesentery from the pieces of pancreas examined in the present study. The present value is in the range reported for other mammalian species (for recent review, see Svanvik and Lundgren).25 From values for sif of 5-10 nl/min together with our observed mean value of 2.45 X lo4 for the number of islets per gram of pancreas and of 6.0 X lo-’ g for the weight of an islet, one obtains values of 0.1% 0.25 ml/min for islet flow per gram of pancreas and 6-17 ml/min for islet flow per gram of islet. According to these results, the partition of direct arterial flow was ll-23% to the islets and 77-89% to the acini (nonislet tissues). The intensity of islet perfusion is in the range of 8-20 times as great as to the acini. We believe that the distribution of spheres resulting from postmortem retrograde administration is strong evidence that virtually all the organ flow going to the islets then distributes to the acini before leaving the organ. Thus, although the arrangement of the direct arterial supplies is quantitatively more in parallel than in series, the fraction of the flow to the islets (ll-23%) is large enough for significant local effects of the islet hormones on the exocrine pancreas via an insuloacinar portal system. There is convincing anatomical evidence that the required channels are present.‘.’ The observations with the microspheres confirm the conclusions drawn from a comparison of the results of arterial and venous administration of India ink or Berlin blue in the older studie?’ as well as more recent ones,“~” of the pancreatic circulatory bed: The islet vessels are easily filled by orthograde injections, but they may not be filled at all by retrograde injections, leaving instead clear areas where islets would be expected. During the final stages of preparation of the pres-
98-99 % of organ weight
-t 5 % of organ welghf [
Figure
100%
6. Diagram of the flow as obtained
= 1.07 ml. mid.
g-1 J
distribution of the pancreatic from the present experiments.
blood
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LIFSON ET AL.
ent paper, Fraser and Henderson”*” published abstracts reporting in vivo observations of the microcirculation in the rabbit pancreas. They state that: “Arterioles supplied islets and exocrine tissue separately, in parallel. However, the outflow from an islet was always through several capillaries into the exocrine capillary meshwork, i.e., the endocrine and exocrine circulations were in series.“” This is a description of Figure ld. Figure 6 adds to Figure ld the quantitative values obtained from the present experiments. Of particular interest is Thiel’s half-schematic drawing of a lobule of the rabbit pancreas as obtained from examination of cleared thick sections of glands injected with India ink7 (Figure 7). In it a single artery penetrates the coneshaped lobule and gives off branches during its course to the tip. If the flows carried by the arterioles leading to islets and acini are similar, this drawing of Thiel’s corresponds not only qualitatively, but nearly quantitatively to Figure 6: The bartition of direct arterial flow would be about three-fourths to the acini and one-fourth to the islets, and all efferent islet flow would go to the acini.
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As in any experiment, the measured value, even if correct, may of course be different from the preexperimental value one wishes to measure, due to procedures involved in making the measurement (anesthesia, surgical intervention, administration of microspheres, etc.). The inference from the microsphere data that most of the pre-islet flow is through vessels 18-22 pm in diameter deserves comment, because it is in apparent disagreement with more direct measurements. In the mouse McCuskey and Chapman” give pre-islet vessels a diameter of 10 f 2.0 (SD) pm in vivo and only 6 f 2.2 (SD) pm in fixed preparations. The values we have measured for these vessels in the stained preparations of the present study or in preparations injected with silicone latex solutions or India ink averaged 10.8 f 3.3 pm (SD; n = 86). However, this direction of discrepancy is expected from the fact that flow is proportional to the fourth power of the radius, at least for streamline flow. For example, if the distribution of flow as a function of vessel diameter is skewed to the right and taken as a gamma distributionz3 with a mean flow-weighted diameter of 18 pm and a coefficient of variation of 0.3,
Figure 7. The half schematic representation of the vasculature of the rabbit pancreas as presented by ThieL7 (Reproduced of Springer-Verlag). The stippled vessels are veins. Two islets are shown.
by permission
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the frequency distribution of geometric diameters would have a mean of only 11 + 4 (SD) pm; and if the flow weighted diameter was 20 pm, the geometric mean diameter would be 12 pm. Much of the discrepancy in question might be accounted for in this way.
References 1. Bunnag SC, Bunnag S, Warner NE: Microcirculation to the islets of Langerhans in the mouse. Anat Ret 146:117, 1963 2. Andrea& G: Die Blutversorgung der Langerhansschen Inseln der menschlichen Bauchspeicheldrttse. Anat Anz 119421, 1966 3. Wharton GK: The blood supply of the pancreas with special reference to that of the islands of Langerhans. Anat Ret 5355, 1932 4. Fujita T: Insulo-acinar portal system in the horse pancreas. Arch Histol Jpn 35181, 1973 5. Fujita T, Murakami T: Microcirculation of the monkey pancreas with special reference to the insulo-acinar portal system. A scanning electron microscope study of vascular casts. Arch Histol Jpn 35255, 1973 6. Fujita T, Yantori Y, Murakami T: Insulo-acinar axis, its vascular basis and its functional and morphological changes caused by CCK-PZ and caerulein. In: Endocrine Gut and Pancreas. Edited by T Fujita. Amsterdam, Elsevier, 1976, p 347357 7. Thiel A: Untersuchungen 6ber das Gefass-System des Pancreaslappchens bei verschiedenen Saugern mit besonderer Berttchsichtigung der Kapillarknauel der Langerhansschen Inseln. Z Zellforsch 39:339, 1954 8. Henderson JR, Daniel PM: Portal circulations and their relation to counter current systems. QJ Exp Physiol 63:355, 1978 9. Beck JSP, Berg BN: The circulatory pattern of the islets of Langerhans. Am J Path01 7:31, 1931 10. Kiihne W, Lea AS: Boebachtigung iiber die Absonderung des Pankreas. Untersuchung Physiol Instit Univ Heidelberg 2448, 1882 11. Fraser PA, Henderson JR: A portal arrangement in the pancreatic microcirculation observed in vivo. Microvasc Res 17 (Part 2):S16, 1979
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of the 12. Heisig N: Functional analysis of the microcirculation exocrine pancreas. Adv Microcirc 1:89, 1968 13. Lifson N, Sircar B, Levitt DG, Lender EJ: Heterogeneity of macroscopic and single villus blood flow in rabbit small intestine. Microvasc Res 17:158, 1976 14. Meschia G, Cotter JR, Makowski EK, Barron DH: Simultaneous measurement of uterine and umbilical blood flows and oxygen uptakes. QJ Exp Physiol52:l. 1967 15. Kramlinger KK, Mayrand RR, Lifson N: Simple method for visualization of the islets in fixed but otherwise intact pancreas. Stain Technol 54:159, 1979 16. Warren DJ, Ledingham JGG: Measurement of cardiac output distribution using microspheres. Some practical and theoretical considerations. Cardiovasc Res 8:570, 1974 17. Androulakis J, Androulakis G, Vezeridis M, Kyriakov K: Arteriovenous intestinal communications in shock. Experimental study using microspheres. Int Surg 601206, 1975 18. Neutze JM, Wyler F, Rudolph AM: Use of radioactive micro-
spheres to assess distribution of cardiac output in rabbits. Am J Physiol 215486. 1968 19. Kaihara S, Van Heerden PH, Migita T, Wagner HN: Measurement of distribution of cardiac output. J Appl Physiol 25:696, 1968 20. Bartrum RJ, Berkowitz DM, Hollenberg NK: A simple radioactive microsphere method for mesauring regional flow and cardiac output. Invest Radio1 9:126, 1974 21. O’Leary JL: An experimental study of the islet cells of the pancreas in vivo. Anat Ret 45:27, 1930
22. McCuskey RS, Chapman TM: Microscopy of the living pancreas in situ. Am J Anat 126:395, 1969 23. Yen RT, Fung YC: Effect of velocity distribution on red cell distribution in capillary blood vessels. Am J Physiol235:H251, 1978 and mesenteric 24. Alexander N, DeQuattro V: Gastrointestinal hemodynamic patterns in neurogenic hypertinsive rabbits. Circ Res 35648, 1974 25. Svanvik J, Lundgren 0: Gastrointestinal circulation. In: Gastrointestinal Physiology II. Edited by RK Crane. Baltimore, University Park Press, 1977, p l-34 26. Daniel PM, Henderson JR: Circulation in the islets of Langerhans (abstr). J Physiol (Lond) 275:1OP, 1978 27. Tohyama M: The blood supply of the pancreatic islets of the dog. Jap J Med Sci 5:81, 1935 28. Fraser PH, Henderson JR The serial arrangement of endocrine and exocrine capillaries in the rabbit pancreas observed in vivo. J Physiol (Lond) 292:4P, 1979
79:408-473,1989
Blood Flow to the Rabbit Pancreas with Special Reference to the Islets of Gngerhans NATHAN LIFSON, KEITH G. KRAMLINGER, MAYRAND, and E. JANE LENDER Department Minnesota
of Physiology,
University
of Minnesota
Nonradioactive microspheres of various sizes (mean batch diameters ranging from 6 pm to 26 pm) were administered to unfasted rabbits under sodium pentobarbital anesthesia by a brief injection into the left ventricle. Flow rate per bead was determined by the reference organ method. After prompt death of the animal, the spheres were located and counted microscopically (islet vs. nonislet) in fixed, stained, and cleared portions of the pancreas. According to an analysis of the distribution of spheres as a function of bead diameter, U-23% of the total pancreatic blood flow went directly to the islets and 77-89% to the “acini” (nonislet tissues). After retrograde postmortem injection of spheres 6 pm, 9 pm and 11 pm in diameter, practically none reached the islets, whereas after orthograde postmortem injection, they did so in the same proportions as in vivo. These results, supplemented by certain control experiments, support the view that all, or nearly all, efferent islet blood jlow goes to the acinar capillaries before leaving the organ. We conclude that the arterial supplies to the rabbit exocrine and endocrine pancreas are in parallel, with most of the flow going to the exocrine portion. However, the jIow to the islets is large enough to permit significant local actions of the islet hormones on the exocrine pancreas, in confirmation of the existence of an insuloacinar portal system. One finds in the literature fundamental disagreements concerning the relationship between the Received August X,1979. Accepted April 8,198O. Address requests for reprints to: Nathan Lifson, Department of Physiology, University of Minnesota, 6255 Millard Hall, 435 Delaware St. SE, Minneapolis, Minnesota 55455. This work was supported in part by U.S. Public Health Service National Institutes of Health Grants AM 19209 and AM 25897. We thank Korey Knutson, Daniel P. Fristoe, and Julie K. Drier for their technical assistance. 0 1980 by the American Gastroenterological Association 0016-5085/80/09046f3-0$02.25
Medical
ROBERT
School,
R.
Minneapolis,
blood supplies of the islets and acini in the mammalian pancreas. For purposes of discussion, the realistically possible topography of the circulation to a pancreatic lobule may be simplified as shown in Figure la, excluding A-V shunts for which there is no evidence. At one extreme is the view that the two supplies are in parallel and practically independent,‘,’ as in Figure lb. At the other extreme is the view that virtually all the blood of the pancreas first goes to the islets and then to the acini. That is to say, except in parts of the gland without islets, the islet and acinar supplies are in series,3-B as in Figure lc, an arrangement constituting an insuloacinar portal system which provides for a local action of the insular hormones at high concentrations on the acini. Intermediate views by otherP add a significant acinar flow to an insuloacinar flow, as in Figure Id, even in parts of the gland with islets. Still another view is that the acinar and islet flows are in parallel, but with communications, as in Figure la.8 Species differences do exist? but they are not responsible for the gross discrepancies among the various proposed arrangements. So far as we are aware, flow from acini to islets has not been directly observed, although its occurrence has been speculated upon in disturbances of the circulation? Thus, at present two fundamental questions concerning the pancreatic circulation are as follows: (a) Of the pancreatic blood flow, how much “normally” goes directly to the islets vs. directly to the acini? And (b) of the fraction going directly to the islets, how much then goes to the acini (vs. bypassing the acini and going directly to veins)? The living acinar and islet circulations were observed microscopically more than a century ago,l’ and a number of times since up to the present.” Red cell velocities in acinar capillaries have been measured,” but otherwise there does not seem to be any quantitation of the flows in question.
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(a)
serw case
P-@-1
33 (b)
Methods
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Intermediate
467
islet capillaries and none in the islets. On the other hand, if the acinar and islet circulations are independent (as in the parallel arrangement, Figure lb), the trapped beads should be distributed between nonislet and islet tissues more or less as they are found to be when entering the organ via the arteries. The conclusions reached will amount to adding the actual values for perfusion to the arrangement of the circulation in Figure Id.
-
Porollel case
BLOOD FLOW
Case
Figure 1. Diagrams of proposed arrangements of pancreatic circulation. a. Realistically possible topography of the circulation of a pancreatic lobule. b. Parallel limiting case. Acinar and islet circulations are completely independent. c. Series limiting case. All direct flow is first to islets and then to acinar capillaries via an insuloacinar portal system. d. Intermediate case. Acinar and islet flows are in parallel, with all efferent islet flow going to acinar capillaries as in c.
It appeared to us that answers to these questions might be obtained by an approach we had used to investigate the intraorgan distribution of blood flow to the small intestine.‘” This approach uses nonradioactive microspheres localized and counted in the intestinal tissues by microscopy. Two different types of experiments will be described, each directed at answering one of the two questions posed, with both types depending on distinguishing between spheres trapped in islets and spheres trapped in nonislet tissue (“acini”). To obtain data bearing on the first question, the microspheres were administered in vivo into the heart, as is conventionally done. To obtain data bearing on the second question, the spheres were administered postmortem by perfusion in the retrograde direction, based on the following rationale. Assume that the spheres are of such a diameter that they would reach the acinar capillaries and be trapped in them if reached, and also assume that the same holds for the islet vessels. Then, to take limiting cases, if the blood supply of the islets is in series with that of the acini (insuloacinar portal system, Figure lc),all the spheres will be trapped in the non-
In Vivo Administration
of Microspheres
Unfasted New Zealand white rabbits weighing about 2 kg were used. The animals were anesthetized by intravenous injection of a combination of 30 mg/kg sodium pentobarbital (Nembutal) and 5 mg of diazepam (Valium). “Carbonized” nonradioactive polystyrene microspheres (Nuclear Products Division, 3M Company, St. Paul, Minn.) were suspended in 0.9% NaCl containing 0.005% Tween 20 (polyoxyethylene sorbitan monolaurate). The suspension was held in an ultrasonic sonicator (ColeParmer, model 8845-3) and shaken by hand before injection into the left ventricle of the heart through a catheter (PE 60) inserted via the left common carotid artery. The arterial blood pressure was monitored by pressure transducer and recorder to ascertain proper positioning of the catheter. Duration of the injection was about 5 set, and the volume injected was 1 ml/kg. Batches of five mean diameters of microspheres were used: “6 pm” (6.1 f 2.0 (SD) pm), “9 pm” (8.9 f 1.1 (SD) am), “11 pm” (10.9 f 1.0 (SD) pm), “16 pm” (16.0 f 1.8 (SD) pm), and “26 pm” (25.8 f 3.4 (SD) w). (The results with “16 pm” spheres will include one experiment with “15 pm” spheres.) The quotation marks will be used to denote a batch of spheres with a given rounded off mean diameter. Cumulative percentage frequency distributions of diameters are shown in Figure 2. The approximate numbers of spheres administered per kilogram of animal were as follows: for “6 pm” spheres, 1Oe;for “9 pm” spheres, 2 X 107;for “11 pm” spheres, 107; for “15 pm” spheres, 7-9 x l@, and for “26 pm” spheres, 106.
A value for the rate of blood flow per microsphere
Diameter
was
in p.m
Figure 2. Cumulative percentage frequency distributions ameters of administered microspheres.
of di-
468
LIFSON ET AL.
obtained by the reference organ methodI by means of a blood sample withdrawn by pump from the lower abdominal aorta at a known constant rate via a cannula inserted into the femoral artery. The blood sample was immediately examined under the microscope for clumping of spheres, and essentially none was seen. The total number of spheres in the blood sample was obtained by counting the number of spheres in aliquots placed on a slide and covered with a glass cover slip. The syringe is in effect an organ of known flow which completely traps the spheres and which is assumed to receive blood identical with respect to bead content to the blood received by the region under investigation. Then the rate of blood flow per sphere becomes the rate of withdrawal divided by the number of spheres in the total withdrawn blood sample. After the microsphere injection and femoral arterial blood collection, the rabbits were sacrificed by intraventricular injection of a saturated KC1 solution. Visualizing both the islets and the trapped spheres was accomplished by sequential in situ arterial perfusion of the pancreas of the sacrificed rabbit with heparinized isotonic saline, formalin, hematoxylin, and water, followed by removal of the tissue for dehydration in ethanol and clearing in methyl salicylate, as described and illustrated elsewhere.” A piece of pancreas about 2 cm* in area was cut from a location within the loop of the duodenum approximately at the level of the main pancreatic duct. Under a dissecting microscope, most of the mesentery and fat was teased away from the piece which was then moderately stretched and made fairly flat so that there were relatively few overlapping lobules. The cleared piece was examined under a dissecting and/or a standard compound microscope to make the following measurements: its area, its thickness in a number of locations, the number of islets in it, the diameter of its islets, the number of islet spheres, and the total number of spheres. Mean single islet blood flow (sif) was calculated from the product of the average number of spheres per islet (which ranged from 0.17 to 0.85) and the reference organ value of flow per sphere. The number of islets per gram of pancreas averaged 2.45 f 0.88 (SD) x 104, and the volume per islet averaged 0.80 nl, from which the total islet volume averaged 1.5% of the organ. Only rarely were islets with diameters less than 50 pm seen, and the smallest were 40 pm in diameter. From the above types of measurements, absolute values were calculated for the arterial perfusion of the organ, its distribution between islets and acini (strictly speaking, nonislet tissue), and the intensity of perfusion of the two types of tissue. Comparisons were made between the microscopic measurements of the volume of the pieces of pancreas carried through the staining and clearing procedures and the volume of fresh untreated pancreas. It was found that the mean volumes calculated in these two ways for a series of 12 pieces were practically identical so that the microscopic determination caused no systematic error. However, the two types of values for the volumes of the individual pieces (taken as equal to weight) differed on the average by 19%. Hence, one can expect considerable rabbit-to-rabbit variability among values expressed per gram of pancreas from this source alone.
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Inherent statistical variability also contributed to the observed rabbit-to-rabbit variability of the results. This contribution was greatest for the values of single islet flow, since only on the order of 70-100 islet spheres were usually counted to provide the values for spheres per islet. However, the observed rabbit-to-rabbit variability was large enough for the inherent statistical variability due to sphere counts to be negligible compared with other sources of variability.
Postmortem Microspheres
Administration
of the
Retrograde postmortem administration of spheres at a dose approximately 10% of the in vivo dose was via a cannula in the portal vein, preceded by a small volume of heparinized isotonic NaCl and followed by 100 ml of the saline. The injection pressures were under 100 cm H,O. The staining procedure was carried out in the usual orthograde direction. Experiments were also done in which all solutions, including the microsphere injectate, were administered postmortem in the orthograde direction. In some retrograde microsphere experiments the procedure was varied in that formalin fixation was retrograde instead of orthograde; in others the perfusate outflows were collected for determination of the number of spheres in them. The distribution of spheres in the pieces of pancreas which received the spheres by postmortem injection, either retrograde or orthograde, was measured somewhat differently than in the above in vivo experiments. Instead of carefully focusing to categorize candidate islet spheres as actual islet spheres, the following less time consuming procedure was used. The total area of a region of the essentially flat piece of pancreas was divided into that seen within the maximum diameters of the islets (“islet area”) and that outside these diameters (“nonislet area”). The spheres within these two areas were counted to give values for the fraction of the spheres in the whole thickness of the region within the islet area, designated as “islet core spheres.” Another measurement made was that of the number of islet spheres seen when the microscope was focused on the equatorial plane of the islets and kept there. The islet spheres seen with this procedure were designated as “equatorial islet spheres.” For comparison, similar measurements were made on tissues from the in vivo experiments. The measure of variability of a mean will be its SE unless otherwise indicated. Statistical significance between mean values was calculated by use of the Student t-test.
Results for Single Islet Flow @if) and Pancreatic Organ Perfusion as Calculated from Spheres of Different Mean Diameters Administered In Vivo Values
Figure 3 is a plot of the values of sif as a function
of sphere
diameter.
Similar
mean
values
were
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DISTRIBUTION
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I 0 0
I
I
1
/
5
IQ
I5
20
, _I51
25
30
00’
0
= 3
’ 5
469
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I
/
/
I
IO
I5
20
25
‘Diameter” of Spheres (Micra)
“Diameter’ of Spheres (Micra) Figure 3. Calculated values for single islet blood flow (sif) as obtained from the administration of microspheres of different batch mean diameters. The measure of variability is the SE. The number of experiments is in parentheses. A value of sif = 0 is plotted at 4 pm because when “6qm” spheres were administered, no injectate spheres less than 4.5 pm were found in the is-
OF PANCREATIC
Figure 4. Calculated values for pancreatic perfusion as obtained from the administration of microspheres of different batch mean diameters. Measure of variability is the SE. The number of experiments is in parentheses. A zero value for pancreatic flow is plotted at 3 pm because when ‘%-pm” spheres were administered, no injectate spheres less than 3.5 pm were found in the tissue.
lets.
obtained with “11 pm” and “16 pm” spheres, 7.16nl and 6.74 nl/min, respectively. The mean value obtained with “9 pm” spheres was about 15% less (5.94 nl/min), but it was not significantly different from However, the value with the larger beads (P > 0.15). a significantly lower flow of about 70% less (2.16nl/ min) was calculated from “6 pm” spheres, the smallest injected. The sif for the largest spheres injected (“26pm”) was zero, i.e., virtually none of these was found in the islets. The value in Figure 3 at 4 pm is also placed at zero, because although approximately 30% of the administered “6 pm spheres were I 4.5 pm in diameter, none of these was found in the islets. The values calculated for sif shauld not be the same for all batches of spheres: Batches of spheres with sufficiently large or sufficiently small “diameters” should both give low values, the large ones because some of the spheres in the batch would not reach the islets, and the small ones because some of the spheres in the batch might shunt through the islets. Batches of intermediate “diameters” would also give low values to the extent that they were subject to both pre-islet trapping and islet shunting. The best estimates for sif, about 7 nl/min, are apparently obtained from “11 pm” and “16 pm” spheres. The question of estimating the true sif from the values in Figure 3 will be considered in the Discussion. Calculated values for pancreatic organ perfusion as a function of mean sphere injectate diameter are plotted in Figure 4. Mean values rise from 0.56 f 0.11 ml * min-’ *g-’ for “6 /.un” spheres to 1.09 f 0.10 ml - min-’ *g-’ for 22 experiments with spheres “9 pm” and larger. Apparently the fractional trapping of “16 pm” and “11 pm,” and even “9 pm” spheres, but not “6 pm”
spheres, was large enough to give values for organ perfusion like those for “26 pm” spheres which do not shunt through the organ.18”’ A value of zero perfusion was assigned to spheres 3 pm in diameter because although more than 10% of the administered “6 pm” spheres were ~3.5 pm in diameter, virtually none was seen in the pancreatic lobules. Results of Postmortem Microspheres
Administration
of
Results of the postmortem administration of “11 pm” spheres are shown in Figure 5. It is seen that when in this type of experiment the spheres were administered in the retrograde direction, only 3-5% 30,
0
OKI 0 12
i
3
:
4
!
5
i
6
I
: s : : ’ 7! 8 9 IQ II 12
% of Area of Piece Occupied
by Islets
Figure 5. Relationship in experiments with “11-pm” spheres between (a) the percentage of pancreatic “islet core spheres,” i.e., those in the whole tissue thickness within the circumference of islets, and (b) the percentage of area occupied by the islets. The line in the figure gives the relationship for random distribution of the spheres in the islets and nonislet portions of the tissue. Ortho = orthograde administration of microspheres. Retro = retrograde administration of microspheres.
470
LIFSON ET AL.
of the tissue spheres were “islet core spheres.” Essentially none of these was an “equatorial islet sphere” (data not shown). Since 5.5-8.0%of the tissue area was within the islet circumference, there were even fewer spheres in the islet cores than would have been found from a random distribution of spheres in islet and nonislet tissue. The plotted points fall below the line drawn in Figure 5 for such random distribution. Apparently few if any of the “11 pm” spheres had reached the islets, consistent with a series portal arrangement of practically all insular flow. The location of the spheres after their retrograde injection was in marked contrast to the findings in the in vivo experiments, in which 15-27% of the spheres were “islet core spheres” when the area containing these spheres made up only 5-8% of the total area, reflecting the greater concentration of spheres in the islets. Actually, nearly all these core spheres were in the islets, since the “11-pm” islet spheres averaged about 20% of the organ spheres. “Equatorial islet spheres” amounted to 8-14% of the total (data not shown). The postmortem orthograde sphere injections described in Methods were done to test for whether a change in the vasculature during the postmortem bead injection might have been responsible for the differences between in vivo and postmortem retrograde microsphere distributions. The results from the postmortem orthograde bead injections were like those from in vivo administration of the spheres (Figure 5).Hence, no evidence was obtained that the state of the vasculature was significantly different in the postmortem experiments with respect to trapping of spheres from that when the spheres were injected in vivo. The findings from use of “9 pm” spheres were similar to those from use of “11-pm” spheres (data not shown), as were the results for the “6-pm” spheres, except that with these smaller spheres the percentage of islet spheres (either “core” or “equatorial”) was less than for the larger spheres. This latter relationship is consistent with the values in Figures 3 and 4 which indicate a smaller fractional trapping of “6-pm” spheres by islet capillaries than acinar capillaries. The results were also similar whether the formalin fixation was by orthograde or retrograde administration before the staining and washing steps with the latter two always being orthograde. Moreover, only small percentages of the administered spheres were recovered from the fluids leaving the organ via the arteries during the retrograde injections or via the veins during the subsequent staining and washing steps. For example, in “11-pm” experiments of this type, 3 + 1% (n = 3) of the adminis-
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tered spheres were recovered in the arterial outflow and 7 + 2.4% (n = 7)from the orthograde venous outflow during the staining and washing perfusions. It is to be noted that the pancreas formed only a small portion of the weight of tissues perfused.
Discussion Correct values for sif depend in the first instance on correct counts for spheres per islet and correct reference blood values for flow per sphere. Aside from inherent statistical effects, to which reference has been made in Methods, incorrect values for spheres trapped per islet would arise if there were unstained (unseen) islets and if the value for spheres per islet were different in these islets from those in the stained (seen) islets. They could also arise if spheres were incorrectly assigned to seen islets. We do not believe that errors of this sort were large because of the appearance of the stained tissues and because the islet numbers and volumes are like those in the literature. There is good evidence that the value for flow per sphere obtained from the abdominal aorta by the reference organ technique should be a satisfactory one.‘e*1e-20 Even given correctly counted spheres per islet and the correct flow per sphere, sizable systematic errors in the values for sif could have been produced if the following assumptions were seriously invalid: (a) that all spheres in the blood destined for the islets reached the islets; (b) that only such spheres reached the islets; and (c) all the spheres reaching the islets were trapped in them. The fraction of spheres in the arterial blood flow trapped in a given vessel bed should be chiefly contingent on two frequency distributions: The first is the frequency distribution of the diameters of the blood spheres. This distribution is known from measurement (Figure 2). The second is the frequency distribution of the probability of a sphere entering the vessels. The microsphere method assumes that this probability is proportional to flow and hence related to a higher power of the diameter (the fourth power for streamline flow). The reported coefficient of variation of the distribution of geometric diameters of pre-islet arterioles and islet capillaries is about 0.25,2*~22and the corresponding coefficient of variation of the frequency distribution of flow as a function of diameter should be only moderately larger. Given this information about the two frequency distributions in question, the results in Figure 3 permit inferences to be drawn with some confidence from rather simple semiquantitative considerations. Thus, that the mean “6 pm” sif is only about one-third as great as the mean “9 pm” sif places the trapping diameters of the islet vessels car-
September
1980
rying most of the flow between 6 pm and 9 pm. In this case all but a small fraction of the “11 pm” and an even larger fraction of the “16-pm” spheres reaching the islets would be trapped in them. Further, since both “11-pm” and “16-pm” spheres yielded similar values for sif, the pre-islet vessels did not distinguish demonstrably within the variability of the observations between these two injectate diameters. In view of the size distributions of these spheres (Figure 2), the diameters of the pre-islet vessels carrying most of the flow to the islets are thus placed at 16 pm and larger; but they are less than about 22 pm since “26-pm” spheres did not reach the islets. Accordingly, it appears that only a small fraction of either the “11-pm” or “16-pm” spheres in the blood destined for the islets was trapped in pre-islet vessels; and, having arrived in islets, only a small fraction failed to be trapped in them and to this extent supported the validity of assumptions (a) and (c) for these spheres. The validity of assumptions (a) and (b) also requires that the spheres be distributed in pancreatic arterial blood in proportion to flow until the blood enters the afferent arterioles of the islets. Effects dissociating volume and sphere flow (such as nonrandom radial distribution of spheres in the blood by inadequate mixing, axial streaming, and plasma skimming; and the flow velocity effect of Fung’“) are undoubtedly occurring to some degree in the microcirculation. We do not know the direction and magnitude of systematic errors in sif produced by these effects. A source of invalidity of the assumptions in these particular experiments which is not present in the usual microsphere measurements of blood flow is the staining procedure. One cannot be sure that the postmortem flows of perfusion fluids in the procedure have not moved microspheres. One reason for believing that such an effect has not been large is that the postmortem perfusion of intestinal wall with silicone latex did not cause detectable differences in the distribution of microspheres in the intestinal tissue layers.13 Another reason is that when the fluid draining from the portal vein during the staining procedure was collected and examined for its content of microspheres, it was found that the total of these spheres were a minor percentage of those remaining in the tissues. If invalidity of the assumptions caused a gross overestimate of sif, say by 50%, the true value would be 2/3 X 7.0, or about 4.6 nl/min. Our subsequent calculations involving sif will be reported as the range obtained by using what seem to us conservatively wide limiting values of 5 and 10 nl/min, bracketing the “best” mean values of 6.74-7.12 nl/min from Figure 3. Validity of the mean value for pancreatic organ
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FLOW
471
perfusion (1.09 -+ 0.10 ml - min-’ 9g-‘) as estimated by the “9 pm” and larger spheres is subject to fewer sources of uncertainty than is the estimate of sif which depends on intraorgan factors. The only requirements are that the values of flow per sphere and spheres trapped per gram of pancreas be correct. The above value is more than double the flows of close to 0.40 ml - min-’ . g-’ reported previously for the rabbit pancreas.“.” Part of the disagreement may be due to the more nearly complete removal of fat and mesentery from the pieces of pancreas examined in the present study. The present value is in the range reported for other mammalian species (for recent review, see Svanvik and Lundgren).25 From values for sif of 5-10 nl/min together with our observed mean value of 2.45 X lo4 for the number of islets per gram of pancreas and of 6.0 X lo-’ g for the weight of an islet, one obtains values of 0.1% 0.25 ml/min for islet flow per gram of pancreas and 6-17 ml/min for islet flow per gram of islet. According to these results, the partition of direct arterial flow was ll-23% to the islets and 77-89% to the acini (nonislet tissues). The intensity of islet perfusion is in the range of 8-20 times as great as to the acini. We believe that the distribution of spheres resulting from postmortem retrograde administration is strong evidence that virtually all the organ flow going to the islets then distributes to the acini before leaving the organ. Thus, although the arrangement of the direct arterial supplies is quantitatively more in parallel than in series, the fraction of the flow to the islets (ll-23%) is large enough for significant local effects of the islet hormones on the exocrine pancreas via an insuloacinar portal system. There is convincing anatomical evidence that the required channels are present.‘.’ The observations with the microspheres confirm the conclusions drawn from a comparison of the results of arterial and venous administration of India ink or Berlin blue in the older studie?’ as well as more recent ones,“~” of the pancreatic circulatory bed: The islet vessels are easily filled by orthograde injections, but they may not be filled at all by retrograde injections, leaving instead clear areas where islets would be expected. During the final stages of preparation of the pres-
98-99 % of organ weight
-t 5 % of organ welghf [
Figure
100%
6. Diagram of the flow as obtained
= 1.07 ml. mid.
g-1 J
distribution of the pancreatic from the present experiments.
blood
472
LIFSON ET AL.
ent paper, Fraser and Henderson”*” published abstracts reporting in vivo observations of the microcirculation in the rabbit pancreas. They state that: “Arterioles supplied islets and exocrine tissue separately, in parallel. However, the outflow from an islet was always through several capillaries into the exocrine capillary meshwork, i.e., the endocrine and exocrine circulations were in series.“” This is a description of Figure ld. Figure 6 adds to Figure ld the quantitative values obtained from the present experiments. Of particular interest is Thiel’s half-schematic drawing of a lobule of the rabbit pancreas as obtained from examination of cleared thick sections of glands injected with India ink7 (Figure 7). In it a single artery penetrates the coneshaped lobule and gives off branches during its course to the tip. If the flows carried by the arterioles leading to islets and acini are similar, this drawing of Thiel’s corresponds not only qualitatively, but nearly quantitatively to Figure 6: The bartition of direct arterial flow would be about three-fourths to the acini and one-fourth to the islets, and all efferent islet flow would go to the acini.
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As in any experiment, the measured value, even if correct, may of course be different from the preexperimental value one wishes to measure, due to procedures involved in making the measurement (anesthesia, surgical intervention, administration of microspheres, etc.). The inference from the microsphere data that most of the pre-islet flow is through vessels 18-22 pm in diameter deserves comment, because it is in apparent disagreement with more direct measurements. In the mouse McCuskey and Chapman” give pre-islet vessels a diameter of 10 f 2.0 (SD) pm in vivo and only 6 f 2.2 (SD) pm in fixed preparations. The values we have measured for these vessels in the stained preparations of the present study or in preparations injected with silicone latex solutions or India ink averaged 10.8 f 3.3 pm (SD; n = 86). However, this direction of discrepancy is expected from the fact that flow is proportional to the fourth power of the radius, at least for streamline flow. For example, if the distribution of flow as a function of vessel diameter is skewed to the right and taken as a gamma distributionz3 with a mean flow-weighted diameter of 18 pm and a coefficient of variation of 0.3,
Figure 7. The half schematic representation of the vasculature of the rabbit pancreas as presented by ThieL7 (Reproduced of Springer-Verlag). The stippled vessels are veins. Two islets are shown.
by permission
September
1980
the frequency distribution of geometric diameters would have a mean of only 11 + 4 (SD) pm; and if the flow weighted diameter was 20 pm, the geometric mean diameter would be 12 pm. Much of the discrepancy in question might be accounted for in this way.
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