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The extractions of 85Sr2+, 18F−, sucrose-14C, EDTA-51Cr, and antipyrine-14C in bone were determined by the multiple indicator-dilution method. Fluoride and strontium extractions were 18 to 70% during a single transcapillary passage, and those of EDTA and sucrose were from 11 to 59%, whereas extraction of antipyrine was 87%. Injections of 85Sr2+ and 18F− made when perfusion was done alternately with blood and plasma resulted in similar fractional extractions. When flow and extraction were measured simultaneously, extraction was related inversely to flow.
The primary objective of this study was to ascertain the transcapillary extractions, E, of fluoride, strontium, sucrose, and EDTA during a single passage through the capillary bed of tibial bone. The tracers fluoride and strontium are of particular interest in bone because of their known uptake and deposition in the crystalline matrix of bone. Because strontium and other tracers are only partially extracted in the capillary bed of bone [1, 2], a particular provocation for our examination of fluoride uptake was the report by Wootton , who used fluoride deposition as a measure of regional bone blood flow on the assumption that its extraction was complete during a single pass through the capillary. Fluoride tracer has been combined with EDTA-51Cr as a clinical method for measuring skeletal blood flow. The assumption behind this technique is that 18F− is completely extracted in a single transcapillary passage. The EDTA-51Cr function is assumed to be equivalent to that part of the 18F− function that reflects tracer movement into the extracellular fluid but not into bone.
The tracer antipyrine is a lipid-soluble molecule that has been shown in previous studies to be freely diffusible across the capillary barrier . Since the maximum extraction of water, for example, in the lung, is not 100% , it would seem unlikely that even antipyrine would be totally extracted. For this reason, comparison of antipyrine with fluoride allows a useful qualitative comparison of a lypophilic substance and a hydrophilic ion.
Six sets of experiments were done (Table 1). The tibial nutrient artery and ipsilateral femoral vein of adult dogs were cannulated for introduction of radioisotopes and collection of venous samples, as described previously [1, 2]. The femoral vein is cannulated for outflow collection. The blood will include that from tissues other than bone, but this merely dilutes the tracers but does not change their amounts or their relative concentrations. Our past studies indicate that the fractional recovery rate of a bone-seeking isotope in such an experimental setup is 99% . Using venous outflow from the limb maximizes the amount of blood collected and gives more accurate results than collecting nutrient vein blood . In the first three sets of experiments, the nutrient artery was tied off proximally. Nutrient artery cannulation does reduce the flows somewhat; earlier studies showed a decrease in diaphyseal 85Sr clearance by one-third . In the last three sets of experiments, the tibial capillary bed was perfused at a chosen constant blood flow by the use of a Holter pump (model A175, 110V, Extracorporal Medical Specialties). The flow was nonpulsatile.
Albumin labeled with 51Cr or 99mTc (Squibb) was used as a non-permeating intravascular reference tracer. The permeant test tracers were carrier-free 18F as the fluoride ion in isotonic saline (Medi+Physics and Phoenix Memorial Hospital, University of Michigan), carrier-free 85SrCl2 (Squibb), 14C-labeled antipyrine in isotonic saline (New England Nuclear), and 51Cr-labeled EDTA (New England Nuclear). The injection mixture consisted of 15 or 60 µCi of 18F−, 15 µCi of albumin-51Cr or 15 µCi of albumin-99mTc, 5 µCi of sucrose-14C, 20 µCi of EDTA-51Cr, and 5 µCi of antipyrine-14C or 5 µCi of 85Sr. In the first three sets of experiments, isotonic saline was injected over a period of 1 min, and in the second and third sets over 47 s, with the use of an infusion pump (Harvard Model 932) for the injection. In the last three sets of experiments, a 1- to 2-s injection of 0.25 ml of injectate was followed by a short flush of 0.1 ml. In the first three sets of experiments, the tracer was injected as an extended bolus at a constant rate into the distal segment; this was done because the blood flow through the tibial diaphysis is collateral flow of about 2.5 ml/100 g/min, estimated from clearance values corrected by net extraction  or estimated by microspheres in standing, conscious dogs . Further, we wished to keep injectate flow to a modest fraction of the total in order to avoid disturbing the rate of flow or the perfusion pressure. Venous outflow dilution curves were obtained from multiple sequential samples from the femoral vein. In collecting the total femoral vein flow, 18 or more sequential samples, each of 5 or 10 s duration, were obtained, beginning with the start of the injection.
For sets four, five, and six, the experimental setup was modified to provide continuous perfusion of the tibial nutrient artery with a Holter pump. The dog was perfused with its own blood, between 200 to 300 ml of which had been removed and replaced with a similar volume of Rheomacrodex. Hematocrits were known in all experiments, and in set five, we perfused the bone alternately with plasma and with blood having a hematocrit of 20%. Multiple dilution curves were obtained in some dogs (Table 1). In the dogs in which multiple curves were obtained, pre-injection standards were taken from the venous blood to correct for residual isotopic activity. They were very low. The volume of blood was noted at frequent intervals so that accurate estimates of flow could be determined. At the end of the experiments, the tibia was removed, cleaned of soft tissue, and weighed. Since hematocrits were known, plasma flow, Fs (ml/100 g bone per min), could be calculated when blood was used as the perfusate.
In these experiments, activity was measured in samples of blood, plasma, and bone. Because an appreciable amount of 18F− could enter the red blood cells , particularly in the minutes between collecting samples and taking aliquots for counting, 1 ml of whole blood was taken from each sample, and the activities of 18F− and 51Cr were determined in a well-type scintillation detector (Nuclear Chicago model C 120-1). The 18F− was allowed to decay out, and then the 1-ml samples of whole blood were recounted. This allowed calculation of the activity due to 18F− and 51Cr. From aliquots that were centrifuged, the activities of 51Cr and 14C were determined in 0.2 ml of plasma by an automatic liquid-scintillation system (Nuclear Chicago Mark II) with the techniques of sample preparation and calculation of activity due to each isotope which have been described previously . Samples of blood were used in the place of plasma in those experiments in which antipyrine-14C was given; these were incubated with 60% perchloric acid and 30% hydrogen peroxide before the addition of the liquid scintillator.
In experiments in which 18F− and 85Sr2+ were used together counting was performed on a Beckman 310 instrument, and before the experiment, the windows to be used were determined with the use of 22Na+, a positron emitter like 18F−. Before the experiment, mixtures of the three isotopes were examined on a multichannel analyzer. The efficacy of counting 18F− at its main peak (0.5 meV) was determined and found to be satisfactory (24%). The windows were set to count 99mTc, the main peaks of 85Sr2+ and 18F− (both 0.5 meV), and the coincidence peak of 18F− (1.02 meV). Spillover of 18F− into 85Sr2+ windows and of 85Sr2+ into 99mTc windows was determined over a wide range of counts. Strontium activity in each sample was determined by correcting for crossover and background, and then again, with improved accuracy, by recounting after the 18F− and 99mTc had been allowed to decay out.
For the comparisons of sucrose-14C and EDTA-51Cr, the albumin-99mTc and EDTA-51Cr counts were determined on a Beckman 310 gamma counter, allowance being made for EDTA-51Cr spillover into the 99mTc window. After 99mTc had decayed out, counts were determined by means of a Packard liquid-scintillation system. Quench data, background counts, counting efficiency, and spillover were determined, and polynomial equations were fitted to these by computer. From these data, counts of sucrose-14C were obtained. Corrections for decay are made for all tracers; this is especially needed in the instances of 18F and 99mTc.
The first stage was to calculate, from the outflow sample counting, the form of the dilution curve. The fraction of the injected dose of tracer appearing in the femoral vein per second, h(t) s−1, was determined as previously described [1, 2], from the outflow concentration-time curve C(t), in counts per minute per milliliter. Because the injection was prolonged, h(t) had the same dimensions as the curve of the probability density function of transit times but not the same shape; in this study, h(t) is not the impulse response but rather the response to a pulse of finite duration. A mixture of two or more tracers is injected into the cannulated tibial nutrient artery. One of these is the intravascular reference tracer. The other tracers are the permeant tracers. By a sampling of venous outflow, it is possible to measure the fraction of the injected dose of each tracer that appears in the outflow per second, hD(t). The femoral vein is cannulated for outflow collection. Although this blood may include blood from tissue other than bone, this merely dilutes the tracers and does not change their amounts or relative concentrations. Previous studies have indicated that 99% of the tracer can be accounted for in this experimental setup . In the last three sets of experiments, the injection was nearly an impulse injection.
The instantaneous fractional extraction, E(t), for each test tracer is calculated from
in which the subscript R indicates the intravascular reference tracer and D denotes a diffusible permeating tracer. When the injection is a long pulse, only the earliest values of E(t) will provide a measure of the unidirectional flux from blood, just as is true for the impulse response. Mathematically, it has been shown  that the extent of intravascular dispersion, either in inflow before the capillary bed or in outflow downstream from the exchange reigon, should have a negligible influence on the observed E(t), even though the forms of the recorded indicator-dilution curves are markedly changed. Thus the interpretation of E(t) and in particular of the highest value, Emax, which occurs fairly early, is not changed by the form of the injection used in these experiments. Choosing the appropriate extraction with which to estimate flux of ions across the capillary barrier is difficult. The form of the curves is seen in Figure 1 for the prolonged injections when the tibia was autoperfused (sets one, two, and three) and in Figure 2 for the short injection into the pump-perfused nutrient artery (sets four, five, and six). For the autoperfused tibias, Emax was the highest value of the smoothed curve of E(t) and always occurred on the upslope of the reference curve, as previously described [1, 2].
The curves in the pump-perfused dogs for which the short, small volumes of injections were used were more sharply peaked (Fig. 2). From a computer analysis of multiple indicator-dilution curves in the heart (Levin, Holloway, Bassingthwaighte, unpublished data), with the use of the cell-uptake model of Rose et al. , and with flow heterogeneity estimated by means of micro-sphere deposition, it is possible to derive a manual method for obtaining the representative E from E(t) from the early part of the dilution curve.
Each curve of E(t) was smoothed by fitting a smooth curve through the data from the 15th to the 40th second; the value E was taken from this curve at the sample time nearest the time when half of hR(t) had passed, which is at either the peak or one sample beyond the peak of the reference curve. These instantaneous extractions are termed ESr, EF, ESuc, or EEDTA.
The tracers strontium, fluoride, and EDTA were retained in the tissue for a long time in comparison with albumin and sucrose. A measure of this retention at any specified time, T, after injection, an integral or net extraction, is given by
After all the reference tracer has washed out, Enet(T) becomes identical to the residue function for the permeating tracer, , which is the fraction of the injectate retained by the tissue.
The first set of experiments, on eight dogs, was designed for estimating E, the extraction for fluoride; the injectate contained albumin, fluoride, and, as an inert but permeating reference, sucrose-14C.
One set of dilution curves of the sort shown in Figure 1 was obtained from each dog. There was first an appreciable delay before the appearance of any tracer. This delay represents the shortest transit time and is the sum of transit time through the nutrient arterial inflow and that through the bone capillary bed, the outflowing veins, and the collecting catheters. The difference in height between the test indicator curve and the reference indicator curve, relative to the height of the reference indicator curve, is the fractional extraction, E(t), at that instant (Eq. 1b).
Accordingly, the curves of E(t) (lower panel, Fig. 1) increase rapidly to a peak (Emax) and then decline because of the back diffusion of permeant tracer from the extravascular fluid compartment to the capillary. In eight such sets of dilution curves, the observed Emax for 18F− was 0.70 ± 0.08 (SD), and the Emax for sucrose-14C was 0.47 ±0.13.
If fluoride entered red blood cells before or during transcapillary passage, the effective flow, Fs, would be different from the plasma flow. Both Fs and the rate at which fluoride enters or leaves red cells would affect its extraction. The second set of experiments along with set five were therefore designed to test whether the presence of red cells affected the extraction of fluoride either in absolute terms or relative to tracers that are known to be carried in plasma, that is, 85Sr2+, sucrose-14C, and EDTA-51Cr.
Two injections were given to each of three dogs, with an interval of 15 min between them. One of each pair of injection mixtures was equilibrated with whole blood for 5 min before injection. In these particular studies, venous samples were obtained from a small catheter (Intramedic PE240) that was inserted into the femoral vein via a tributary. A pump (Holter RL 175) was used to give a venous sampling rate of about 30 ml/min. Results are summarized in Table 2.
This third set of experiments concerned the extractions of fluoride and antipyrine. The antipyrine served two purposes. One was to provide an estimate of the maximum extraction that might occur with a flow-limited indicator. Previously it was shown that the washout of antipyrine is apparently flow limited and is not permeability or diffusion limited [4, 13]. The other purpose was to compare 18F− with a tracer that equilibrates essentially instantaneously with erythrocytes, for the effective Fs for antipyrine is the flow of whole blood, FB. (Actually, it is slightly less, since at equilibrium the concentration of antipyrine in erythrocyte water is 1.1 times that in plasma water , but there is only 0.74 ml/ml water in red blood cells compared with 0.96 ml/ml in plasma, so that FAP = FB [(1 − hematocrit) + 1.1 hematocrit (0.74/0.96)].)
One nutrient artery injection of albumin, 18F−, and antipyrine was made in each of eight dogs. A set of outflow dilution curves is shown in Figure 3. For the eight dogs, the Emax was 0.65 ± 0.13 for 18F− and 0.87 ± 0.05 for antipyrine.
The fourth set of experiments represents a group of experiments that were performed to establish the method of perfusion (Table 3 and Fig. 4). The fifth set of experiments provides comparison between the two ions F− and Sr2+ in the same dog. We perfused the bone alternately with plasma and with blood having a hematocrit of 20% (Table 3).
The injections were of about 1-s duration; a set of dilution curves is shown in Figure 2. In each of two dogs, five sets of dilution curves were obtained—three with plasma perfusion and two with blood perfusion—giving a total of 10 comparisons. Of the 10 curves, 8 showed E(t)s that increased continuously through the main part of h(t), from about the 15th to the 40th second.
Values for E are given in Table 3. There was no systematic influence of the presence of red cells on E.
Values for Enet(t), calculated by Eq. 1b and illustrated in Figure 2, showed that a greater fraction of fluoride was retained than of strontium at times up to 3 min. The paired values of Enet (2 min)—dogs H159 and H236, Table 3—show 29% retention for F− and 34% for Sr2+ at this time when the albumin had nearly completely washed out. Values for EF, ESr, and Enet for these experiments are illustrated in Figure 4.
The final set of experiments, set six, was a comparison between two molecules of similar molecular weight—EDTA-51Cr (molecular weight 336) and sucrose-14C (molecular weight 342). EDTA is a positively charged molecule and sucrose is without charge. Their volumes of distribution in canine tibial cortical bone are known; that of EDTA is approximately twice that of sucrose or inulin, tracers employed by us to identify the extracellular fluid space of bone [15, 16].
The main observations are that none of the ions or molecules is completely extracted during a single passage. A substantial fraction of fluoride, strontium, and EDTA is retained in the large extravascular volume of distribution of these substances by the end of 2 min. This is less so in the instance of sucrose.
The estimates for extraction of antipyrine, 0.87, are consistent with the maximum extraction for other tracers in situations in which the exchange is entirely flow limited—for example, water in the pulmonary circulation —and what we would expect in view of our earlier observations , that iodoantipyrine is flow limited in its washout from the tibia. The relatively low extraction for fluoride compared with iodoantipyrine suggests that its exchange should be barrier-limited, presumably at the capillary membrane.
It might be argued that the extraction of antipyrine is greater than that of 18F because of its lipophilic qualities so that it might avidly bind to fat marrow. However, this would be the case only if the oil:water solubility ratio of antipyrine were high. This is the case with regard to the tracer xenon-133, and for that reason we have used a lipophilic tracer, antipyrine, which has a much lower oil:water solubility ratio than xenon-133 [17–19]. Recent experiments indicate that the blood-cortical bone partition coefficient, λc, is 0.27 and the blood-marrow partition coefficient, λm, is 0.17. These values were derived from two previously reported studies [20, 21]. They are consistent with the water content of cortical bone determined by steady-state experiments with tritiated water  and the water content of tibial marrow determined by desiccation .
Regarding the radionuclides 85Sr and 18F, it is conceivable that these tracers might concentrate in areas of bone formation or low density, sometimes referred to as “hot spots.” Autoradiographic studies [23, 24] have shown that during the first 10 min after injection of radionuclides, tracer uptake is seen about the surface where vessels are known to traverse, as illustrated in Figures 1 and and22 of the article of Pasternak et al. , and not about areas of low density.
Problems of methodology include the use of albumin as a reference tracer, the choice of the appropriate extraction value, and the role marrow tissue might have in extraction of tracer.
The appropriateness of albumin as a reference is dependent on its escape from the capillary bed being less than 2% on single passage. Its use is not at all negated by Owen and Triffitt’s observation  in young rabbits that the clearance of albumin is about once per hour; this translates to (PS/VISF)alb = 1 h−1 = 2.8 × 10−4 s−1, which is low compared with that estimated for sucrose from this study—about 4.3 × 10−3 s−1. This value was derived as follows:
Considering that Owen and Triffitt emphasize that permeation of albumin is about 10 times greater in young than in adult rabbits (see Fig. 8 in ref. 25), we can anticipate that in our experiments the maximum extraction of albumin could not be more than 2%, which would not invalidate its use as a reference tracer.
When first planning this study of fluoride and strontium extraction, we recognized that fluoride might enter erythrocytes coming from the collateral vessels to mix with the injectate before transcapillary passage. This meant that we would not know whether there was a “red blood cell carriage effect” , whether fluoride exchange with red cells was rapid, or whether the flow, Fs, for fluoride was the same as for sucrose or somewhat greater; thus we knew that information on these points should be obtained before comparison of extraction of fluoride with flow.
From the data of Tosteson  on beef erythrocytes, one would have thought that fluoride might enter erythrocytes within seconds. However, our perfusion experiments with and without red blood cells do not support this idea. The answer may be that the red blood cells of dogs are quite different from those of cows and sheep. This would not be wholly unexpected, because the potassium concentration in the red blood cells of dogs is only 10 mM, compared with 136 mM for humans . Also, Dalmark  observed that, of all the halides, fluoride produces the least inhibition (both competitive and noncompetitive) of chloride transport in human red blood cells, a finding that suggests that fluoride transport by the chloride carrier may be minimal. It would be desirable to have a direct experiment on fluoride uptake in dog red blood cells, preferably with a rapid-reaction apparatus.
If there is rapid entry of fluoride, the value Fs for fluoride would be increased to about 1.12 Fplasma; that is, in the 20% hematocrit experiments, it would be Fplasma 0.8 (0.65 × 0.7 × 0.2 + 0.8), in which 0.65 is the water fraction of red blood cells, 0.7 is an expected Donnan factor, and 0.2 is the hematocrit. Such an occurrence would not change the relationships observed in Figure 4. Although there may be increased solubility of F− for endothelial cells and the cells of bone, this ion is not freely diffusible in the sense that antipyrine is, and therefore there is some limitation of diffusion at the capillary barrier.
It would appear that there is a disadvantage in employing fluoride tracer similar to that in using strontium tracer—namely, that 18F− measures clearance and not flow. At flows similar to those we have observed in the tibial diaphysis of the conscious dog—2.5 ml/100 g/min—net extraction is about 0.30 (Fig. 4).
Concerning marrow effects on tracer uptake, the microvasculature of the tibial diaphysis is composed of the capillaries of the Haversian canals. The marrow of mature dogs is a fatty marrow and serves mainly as a supporting structure for conduit vessels entering and leaving the cortex . Cortical bone forms the major fraction of the mass of the tibial diaphysis, 0.90 . Furthermore, uptake of 45Ca by dog tibial marrow after perfusion into the nutrient artery is small and is only 0.4% of total bone uptake . It is recognized that a tracer injected into the nutrient artery will reach the capillary beds of marrow tissue as well as bone tissue. However, studies with microspheres indicate that the percentage of blood flow to bone tissue in a mature dog tibia is approximately 89%—that is, flow in the tibia is mainly to bone . Thus we do not believe that the presence of blood flow to marrow influences our interpretation.
Studies in this laboratory by Morris et al. [16, 22] have shown that the volume of distribution for EDTA-51Cr is twice that for sucrose-14C—0.0758 ml/ml compared with 0.0429 ml/ml. EDTA does not enter the cell, and it seems unlikely that the chromium-51 label separates from EDTA in competition with calcium . The stability constant for CrEDTA is 1023.4, compared with 1010.6 for CaEDTA [33–35]. Furthermore, studies by both Lopez-Curto et al.  and Morris et al.  indicated that the concentration of 51Cr in blood was the same in dogs with ligated kidneys at 3 and 4 h.
Therefore, the lower net extraction for EDTA-51Cr compared with sucrose-14C is likely due to a larger volume of distribution for EDTA, resulting in less back diffusion of tracer. In view of these observations, plus the close agreement between the volume of distribution of inulin (0.0420 ml/ml) and that of sucrose (0.0429 ml/ml) in bone, we are led to view with skepticism the use of EDTA as an extracellular fluid space marker of bone .
This investigation was supported in part by Research Grants AM-15980 and HL-19139 from the National Institutes of Health, Public Health Service. The authors are grateful to Glenn Christensen for technical help and Rose M. Garmers for preparation of the manuscript.