Upsala J Med Sci 78: 145-149, 1973 An in-vitro Method of Investigating the Rates of Transcapillary Exchange and Net Filtration by Single-injection Technique BO ABERG and SVEN-OLOF LINDAHL From the Institute of Physiology and Medical Biophysics, Biomedical Centre, University of Uppsala, Uppsala, Sweden ABSTRACT A method of preparing a cat's hind leg that is suitable for studying the rates of transcapillary solute and solvent movements is described. The preparation may be perfused at any desired venous pressure. A bolus may be injected into the capillary network without altering either the perfusion pressure or the flow rate (while continuously recording the weight of the isolated leg). A new method of calculating extractions is introduced. This method uses the estimate of the correlation between the relative eon- centrations of reference and test substances in the venous outflow. INTRODUCTION The Starling concept of paracapillary fluid circula- tion is well known. However, in studies of the movement of uncharged molecules from within the capillary to the extravascular space of the tissue, the effect of a transcapillary fluid flow on diffusion has all too frequently been ignored. One result of this omission has been that in ex- planations of the transcapillary separation between uncharged molecules of different sizes the pos- sibility of the diffusion being modified by bulk flow has often been overlooked. This report describes an experimental approach suitable for examining whether the effects of con- vection on diffusion may be disregarded in ac- counting for the transport of uncharged solutes in the capillary bed of a hind leg a cat. METHODS Preparation Cats were anaesthetized with chloroform (30 mg/kg body weight intravenously). isolated from and NembutalB An amount of heparin just sufficient t o prevent coagulation (about 10 000 IU) was administered. After the paw was removed, a circular incision with a cautery was made in the skin ' j u s t below the inguinal ligament and just above the greater 10 - 732853 trochanter. By blunt dissection, all muscular bundles were freed and cut down lo thz hip joint. Ligatures were care- fully tied around each muscle to prevent bleeding. With the excep:ion of the femoral artery and veins, all vessels were ligated separately. After the leg was exarticulated, the animal was bled. Mean-while the femoral artery and vein of the leg were cannulated, the pareparation was laid o n a balance (with an accuracy of 25 mg), and attached to the perfusion equipment, as shown in Fig. 1 a and b. From a reservoir the thermostated-controlled and oxygenated blood of the cat was circulated by a variable-speed peristaltic pump through the arterial and venous vessels, by-passing an injection loop, and returned to rhz reservoir, by-passing a sampling loop. The mean blood-perfusion flow was about 15 ml/min. Papaverin (usually around 60 mg) was introduced into the blood to produce a maximal dilatation of thz blood vessels of the preparation, which was reached when an additional dose of papaverin did not furiher decrease the perfusion pressure. The venous pressure depended on thz lengths and diam- eters of the outflow catheters. Apparatus The experiment was started with the venous blood flow- ing thrsugh C (Fig. 1 b). When th: leg weight was con- stant and th: venous pressure stable, an injection was given by switching the arterial blood flow through th: injecticn loop, which contained the bolus (tube A, Fig. 1 b). As soon as possible after the injection, the outflow was switched to route C-D-E for sampling. About 30 samples were taken during th- venous passage of cne bo- lus, which on the average lasted for 20-60 sec. By changing the venous outflow route from C t o F-D with E closed, the venous pressure increased. This in- crease was controlled by varying the length a n d / o r ths diameter of the catheter. This procedure caused the tissue to become oedematous. After a few seconds, when the leg weight increased at a constant speed and the venous pressure was again stable, a new bolus was injected and collected by opening E. The bolus in the injection loop comprised a mixture of five parts of homologous blood, one part of glucose and raffinose (about 930 m M of each) and on: part of 3 mg/ml Evans blue in physiological saline, which served to label the albumin. The injection loop contained about 1.3 ml. Upsala J M e d Sci 78 146 B . dberg and S . - 0 . Lindahl W D Recorder Force - transducer Fig. I a. A schematic drawing of the ex- perimental set-up. The hind leg of a cat is placed o n the balance and the arterial and venous cannulae are connected to the femoral artery and vein. Leg weight (oedema formation) and arterial and venous pressures (PA and PV) are measured, and the frac- tion collector is connected to the event marker on the recorder for measuring sam- pling time. The thermostate-controlled and oxygenated blood is circulated through the leg via the injection and sampling device (ID) shown in Fig. 1 b. Analyses 1. Venous-outflow concentration curves, as shown in serial samples of the outflow, each about 250 in Fig. 2, in which the concentrations were given as relative volume, were collected in small, weighed glass which to the concentrations in the injection solution (relative were then weighed again and immersed i n 2.00 ml of concentrations). physiological saline in centrifuge tubes. After the mixing, 2. The relative concentrations of raffinose and glucose aliquots were analysed for glucose by a g~ucose-oxidase plotted against the relative concentration of albumin la- method (1, 6 ) and for raffinose by determining fmctose belled with Evans blue for each sample, as shown in Fig. after a Seliwanoff reaction (8). The remainder was centri- 3. The Plots appeared to lie o n straight lines, and the fuged and the analysed for E~~~~ blue at 610 regression coefficients were calculated according to Bart- nm in a Zeiss PMQ spectrophotometer. lett ( 2 ) . The lines pass close to the origin, which means The three measurements mentioned above were made that the regression coefficient equals c a / c , , where cd is on ( a ) blood s a m p ~ e s drawn prior to the bolus injection the concentration of the diffusible and c, that of the (“blanks”), ( b ) the bolus itself, and (c) the serial samples reference substance. from the venous outflow. 3. Extractions calculated according to the formula E = (c,-cCd)/c, o r l - c d / ’ c , ( 3 , 4 , 5). Thus, extraction can be calculated from the regression coefficient in Fig. 3. Ex- traction expresses the fraction of the total amount lost CALCULATIONS The were carried out with the help of a from the bolus or any part thereof, which was eliminated digital computer (CD 3600 or IBM 370) and were Pre- f r o m the blood through the capillary wall. sented in the following forms: to pressure transducer from pump - -+ to artery 4 to sampling from vein Fig. I b. The injection and sampling device. Upper catheter is “arterial”. Blood goes via either route A (injection) o r route B. Below the “venous” catheter is shown; Route C, free flow; Route C-D-E, sampling in free flow. Route F includes a thin ex- changeable catheter producing venous con- gestion with or without sampling. Upsala J M e d Sci 78 Investigating rates of transcapillary exchange 147 25 20 15 10 5 n Yo of injection conc. X A Glucose 0 Raffinose x Evans blue 0 5 10 15 20 rn\ Fig. 2. The relative venous concentrations of albumin (tagged with Evans blue), raffinose and glucose in bal- anced-weight conditions (no net filtration), presented ac- cording to Chinard and Crone (4, 5, 6 ) . DISCUSSION Methods The preparation combines some of the qualities of those previously described (5, 7). One important problem is whether or not the perfused organ has suffered from the operation technique. Fortu- nately, most preparations were successful, in the sense that they were in weight balance (no oedema formation). This balance could be maintained for hours, provided the blood was well oxygenated. Occasionally, however, some preparations showed a slow but steady oedema formation, even when the venous pressure was negative. These prepara- tions were discarded. I n order to obtain a homogeneous distribution of the bolus within the arterial vessel leading to an organ, the injection has to be fairly rapid. When this is given by a syringe, such a rapid in- jection is accompanied by a transient change in both blood pressure and flow. It cannot be safely assumed that this has any effect on the exchange between capillary and tissue. When the injection is given by a separate injection loop, such transi- ents are avoided or at least made small enough not to be detected by the arterial-pressure trans- ducer. Although the bolus concentration is 540 mM and might therefore be expected to cause a loss of water from the tissue, only in one instance was there even a slight leg-weight decrease (about 3.4 x g/sec, 100 g tissue). The explanation of this might be that the reflection coefficient for raffinose and glucose are so low as to have little osmotic effect across a capillary wall. These sugars might rapidly disappear from the blood stream, and the bolus thus behaves as if it were virtually isotonic in the exchange capillaries. C o n c . diff. , Identity l i n e 25 20 15 10 5 / / Raffi nose Glucose Raffinose & Glucose (congested) A Raffinose 4 Glucose Conc. ref. 5 10 15 20 25 Fig. 3. The relative concentration of the diffusible molecule (conc. diff.) plotted against the relative con- centration of the reference (conc. ref.). The continuous lines are the best fit of straight lines calculated according t o Bartlett (3). The angles of inclination of these lines are used to calculate the extractions. Note that during rapid oedema formation (raffinose and glucose (congested)) the extrations of raffinose and glucose are of about the same magnitude. Upsala J M e d Sci 7% 148 B . Aberg and S . - 0 . Lindahl Calculations The slop: of the regression line between reference and test-solute concentrations in the venous out- flow is Acd/Ac,.. This ratio differs from the ratio c,/c, if the line does not pass through the origin. There are three possibilities for cd not t o be zero when c, is zero: 1. The diffusible substance passes back from the tissue to the blood (back diffusion or back transport). If this blood-tissue-blood transport were slower o r faster than the intravascular passage of the bolus through the exchange vessels, there would be a time-lag between the venous appear- ance of the reference and test substance (compare the results in ref. (9)). In this case, the cd/c, ratios would not fall on a straight line but would form a loop. Fig. 3, however, showed no sign of such a loop. 2. The reference substance follows an axial stream in the blood, whereas the test solute does not. In that case, there would also be a different appearance time between the “faster” reference solute and the test solute. For the substances used, this possibility seems excluded. 3. The base-line in Fig. 2 has not been deter- mined correctly. This would appear as a constant addition to the regression line (a parallel displace- ment of the regression line), if the concentration ratios fall on a straight line. In that case, the cal- culated ratio A c d / A c r would probably be a more reliable estimate of the extraction than the ratio The advantage of this extraction-estimate meth- od (regression method) is its simplicity. I t further gives information about the constancy of the ex- traction, it rules out the errors in concentration measurements a t the beginning and the end of the venous-outflow-concentration curves, as these points bear little weight in calculating the regres- sion line, and lastly it involves the possibility of excluding errors in base-line determinations. Whatever method is used for calculating ex- tractions, the values obtained will be erroneously low if the reference substance leaks out from the vessels. In that case, the concentration of the ref- erence solute in the venous outflow must be cor- rected by multiplying by a correction factor (1 + the lost fraction of the reference substance). Whether or not such a leak of the reference sub- stance used in the work described in this paper occurs will be further investigated. Upsala J M e d Sci 78 c d / cr. Preliminary results In the balanced-weight condition (when the per- fused leg suffers no net change in weight during the bolus passage), the relative amounts of glucose and raffinose lost to the tissue seem proportional to their diffusion coefficients in free solution and the results seem to confirm those of Crone (5) (Figs. 2 and 3). I n the experiment cited here, the (raffinose/glucose) extraction ratio amounted to 0.65, which equals the free diffusion coefficient ratio (0.434/0.673 = 0.645). On the other hand, when there is venous con- gestion, the loss of both raffinose and glucose is increased. With increasing speed of oedema forma- tion, raffinose is lost relatively more quickly than glucose, until the differences in their relative concentrations in the venous outflow finally vanish (Fig. 3). The preparation described here and the regres- sion method of calculate extractions is to be used in further studies of the transcapillary transport of raffinose and glucose, both in stable weight conditions and during oedema formation. ACKNOWLEDGEMENTS This work was supported by grants from the Medical Faculty, Uppsala University, the Swedish Medical Research Council (Project No. 14X-629) and the National Institutes of Health (Grant No. 5 R 0 1 H E 12960-08). The authors also wish to express their gratitude to miss Carin Ferner for valuable technical assistance. This paper was translated by Neil Tomkinson. REFERENCES 1. Aberg, B.: Interference of light o n the determination of low glucose concentrations with glucose exidase. Acta Physiol Scand 71: 186-193, 1967. 2. Bartlett, M. S.: Fitting a straight line when both vari- ables are subject to error. Biometrics 5: 207-212, 1949. 3. Chinard, F. P. & Enns, T.: Transcapillary pulmonary exchange of water in the dog. Am J Physiol 178: 197- 202, 1954. 4. Crone, C.: O m diffusionen af nogle organiske non- elektrolyter fra blod ti1 hjernevaev. (Thesis.) Munks- gaard, Copenhagen, 1961. 5. Crone, C.: The permeability of capillaries in various organs as determined by use of the “Indicator diffusion” 6. 7. method. Acta Physiol Scand 58: 292-305, 1963. Keilin, D. & Hartree, E. F.: Specificity of glucose oxi- dase (Notatin). Biochem J 50: 331-334, 1952. Pappenheimer, J. R. & Soto-Rivera, A,: Effective os- motic pressure of the plasma proteins and other quantities associated with the capillary circulation in the hindlimbs of cats and dogs. A m J Physiol 152: 471- 491, 1948. Investigating rates of transcapillary exchange 149 8. Roe, J. H., Epstein, J. H. & Goldstein, N. P.: A photometric meth3d for the determination of inulin in plasma and urine. J Biol Chem 78: 839-845, 1949. 9. Martin, P. & Yudilevich, D.: A thzory for the quantifi- cation of transcapillary exchange by tracer dilution curves. Am J Physiol 207: 162-168, 1964. Received February 17, 1972 Revised Mars IS, 1973 Address for reprints: Bo Aberg Institute of Physiology and Medical Biophysics Uppsala University Biomedical Center Box 512 S-751 23 Uppsala 1 Sweden Upsala J M e d Sci 78