II 1] HI THS ERELSURE‘FLQWa DISYENEKEN RELETIQILHEPS 59:! WEE £3336 i’fii‘aé‘éEY Thmés i‘c‘r Ma Basra of 92%.. 3. "INCH C3136 S“ E u u‘JERS "‘t‘ 2g ’ f "'9. km bu: W. $93.83 tam-£2» :1‘ -/3 ., 39:053.“- IfiESI’S kl; LIBRARY Michigan State University PRESSURE—FLOW-DISTENSION RELATIONSHIPS IN THE DOG KIDNEY By CLYDE REYBURN REPLOGLE AN ABSTRACT Submitted to the College of Science and Arts Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Physiology and Pharmacology 1960 I Approved by %M W ABSTRACT Little information is available concerning the control of distension of the kidney even though a possible relationship has been suggested between dis- tension of the kidney and renal hypertension (Swann, 1959). The work reported here is an effort to describe the control of distension and its relationship to renal dynamics in general. The experiments were performed using an isolated dog kidney, suspended in a perfusion chamber, perfused by the circulation of the donor dog. Pressure and flow were measured by conventional techniques, and kidney weight was measured by suspending the kidney from a Statham strain gage inside the perfusion chamber. Distensibility was derived by a technique which involved occluding the renal artery and applying a variable venous hydrostatic pressure. This static technique equilibrated the pressures throughout the kidney so that the venous hydrostatic pressure was the same as the pressure at the site of formation of interstitial fluid. The fluid is formed at the peri- tubular capillary bed. The pressure at the site of formation is the pressure which will determine the volume of the kidney. This has been called the "distending pressure”. Hhen the amount of distension and the distending pressure are known, a distensibility can be calculated. 11 It was found that the distension of the kidney was linear in three phases with the distending pressure. The first phase was interpreted as the filling of the vascular tree. This was more easily filled than the interstitial space which was interpreted to be the second phase. After the interstitial space was filled, the kidney capsule had to be stretched which represented the third phase. The distensibility of the capsule was shown to be inversely proportional logarithmically to the age of the dog. It has been shown by Wells (1960) that the dis- tension of the kidney and autoregulation of blood flow are controlled by a changing venous resistance. In light of this finding, a study was made in an effort to determine the physical relationships necessary for this venous resistance. A model was constructed using a non-elastic collapsible tube to simulate the venous circulation. The construction was such that the pressure gradient from one end of the tube to the other could be controlled and a collapsing pressure could be applied. It is seen in this model that an increase in collapsing pressure causes an increase in resistance regardless of the transmural pressure. It was also found that the closing pressure was within one cm. of water of the collapsing pressure. It is postulated from the work of v.11: (1960) and the author, in this present study, that 111 autoregulation, distension, closure of vessels, and resistance changes due to aging in the kidney are dependent upon the tissue pressure. iv REFERENCES Swann, H. G., Railey, M. J. and Carmignani, A. E., (1959) ”Functional Distension of the Kidney in Perinephritic Hypertension". Amer. Heart J., 58, 608-622 wells, C. H. (1960) ”Estimation of Venous Resistance and their Significance to Autoregulation in Dog Kidneys". Master's Thesis, Michigan State University ACKNOWLEDGMENTS The author is indebted to Dr. W. D. Collings, who contributed his time generously both in the laboratory and in the preparation of this manuscript. The author is also indebted to two colleagues, Charles wells and E. J. McCoy, who contributed heavily to this experiment. Acknowledgment is also made to the author's wife, whose long hours of patient labor made this manuscript possible. vi PRESSURE—FLOW-DISTENSION RELATIONSHIPS IN THE DOG KIDNEY BY CLYDE REYBURN REPLOGLE A THESIS Submitted to the College of Science and Arts Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Physiology and Pharmacology 1960 INTRODUCTION AND SURVEY MATERIALS AND METHODS CALCULATIONS RESULTS AND DISCUSSION Distensibility Studies on a Model SUMMARY AND CONCLUSIONS APPENDIX A APPENDIX B REFERENCES 0 O 0 TABLE 0 OF CONTENTS OF LITERATURE O O 0 O of Venous viii O O Page 1h 17 17 26 37 38 45 1&7 LIST OF TABLES Table Page 1. Relationships between Distensibility and Age . . . . . . . . . . . . . . . . o o o 0 2h 2. Static Weight and Distending Pressure Measurements . . . . . . . . . . . . . . . 39 3. Pressure, Flow, and Weight Measurements with Calculated Distending Pressure and Resistance . . . . . . . . . . . o . . . . #1 h. Weight and Time Measurements . . . . . . . #3 5. Pressure and Flow Measurement for Physical Model . . . . . . . . . . . . . . o . . . . an 60 Table Of Symbols o o o o e o o o o o o o o 1‘6 ix LIST OF FIGURES Figure l. 2. 3. h. 5. 6. 7. 8. 9. 10. ll. Diagram of Perfusion Apparatus . . . . . . Distension - Distending Pressure Curves . Distension — Time Relationship after Increase in Arterial Pressure . . . . . . Log Distension - Time Curves . . . . . . . Log 8 - Age Relationship . . . . . . . . Diagram of Venous Resistance Model . . . . Pressure - Flow Curves for Model . . . . . Log Pressure - Flow Curves . . . . . . . . Pressure - Flow Curves for Autoregulating Kidney . . . . . . . . . . . . . . . . . . Log Pressure — Flow Relationship . . . . . Illustration of Pulsating Venous Pressure. Page 10 18 19-20 21 26 28 29 30 31 35 INTRODUCTION AND SURVEY OF LITERATURE It has been known for many years that the kidney in its functional state is distended to a greater extent than the excised organ. This has been called "functional distension" by Swann (1955a). Swann (1952) showed that the kidney loses about 22% of its volume through drainage from the vein following arterial occlusiOn. He also showed that the fluid which drains from the functionally distended organ has an hematocrit which is 67% of the arterial blood hema- tocrit (Swann g£_alt,1955a). Swann (1959) has theorized that when the normal (functional) distension of the kidney is limited, the animal becomes hypertensive. He incarcerated one kidney in a stiff collodion hull and performed a contralateral nephrectomy after the procedures of Soskin and Saphir (1932). This produces malignant hypertension in about seven days. He found that the interstitial pressure, in the incarcerated kidney, increased from the normal level of 26 mm.Hg to 100 mm.Hg by the second day. He found that with the rise in interstitial pressure, there was a 62% decrease in normal distension. Swann stated, "Encroachment by compensatory hypertrophy (after contralateral nephrectomy) in the naturally distended spaces is thought to have caused the hypertension." In the present theory, proposed by Swann (1959), all experimental and natural causes of renal hypertension are explained by reduction in functional distension of the kidney. The work of Soskin (1932) which used the incarcerating hull is ex- plained above. Hypertension produced by the method of Page (1939), using a cellophane wrap to produce peri- nephritis, is explained by contraction in renal inflam- mation. Goldblatt (1938) produced experimental hyper- tension by means of partial renal arterial occlusion with silver clamps. These results are explained by a reduction in the inflating pressure. Although the possibility of a relationship between the functional distension of the kidney and renal hypertension has been inferred, very little work has been done to show the control of distension. The initial observation that distension of the kidney varies with blood pressure was made by Swann (1955b). He determined that if the kidney volume was taken to be 78% at zero arterial pressure, the volume would increase to 100% at 70 mm.Hg and to 110% at 200 mm.Hg arterial pressure. If distension (maintenance of a large inter- stitial Space of the kidney) is the factor which is associated with renal hypertension, information con- cerning the control of renal distension would be important. The problem of pressure control of dis- tension is, of course, essentially the same as the problem of pressure control throughout the kidney. Complete information concerning the relationship of the renal dynamic system with the distension of the kidney becomes desirable. A great deal of information concerning the renal dynamic system is now available. It has been known for some time that the kidney exhibits an "autoregulation" of blood flow, i.e. when blood pressure increases at the renal artery, resis- tance to flow in the kidney increases and blood flow is held more or less constant. Selkurt (19h6) using PAH clearances as a deter- mination of blood flow found that the resistance of the kidney increased with pressure. This was confirmed by Forster and Mass (19h?) who stimulated the carotid sinus reflex. They found a “3% increase in arterial pressure and only a 5% increase in renal plasma flow. Selkurt (1955) presented extensive evidence that autoregulation of renal blood flow was intrinsic to the kidney. Hinton (1951), Forster and Macs (19h7). and Shipley and Study (1951) showed that an increase in .filtration fraction at the glomerulus and the subsequent increase in viscosity could not account for the increase in resistance. A mechanism involving an increase in the geometrical component of resistance had to postulated (Raddy, 1958). However, Raddy did not specify the nature of the component. Hinton (1951) suggested that the increase in kidney resistance had to be preglomerular because there is an autoregulation of glomerular filtration rate and a con- stant arterio-venous oxygen difference. Haddy (1958) points out that the resistance must be active rather than passive because Hinton (1951), Gottschalk (1952), Swann (1952), Miles and de wardener (195a), and de Langen (1957) have shown that the rise in interstitial pressure with a rise in arterial pressure is, at most, 15% of the rise in arterial pressure. Another theory was advanced in 1952 by Pappenheimer (published in 1955). His theory states that the plasma is skimmed from the blood in the increasingly smaller vessels of the kidney in such a manner that the cell- poor fraction goes through the glomerularmperitubular vessels and the cell-rich fraction shunts the majority of the kidney tissue, possibly in the juxtamedullary region. The degree of skimming would increase as the velocity of blood flow increased. In this system, the resistance of the kidney would depend on the re- sistance of two parallel circuits. The cortical circuit is supplied with blood containing 10% red blood cells and the shunt circuit with blood containing 80% red blood cells. The viscosity of the cell-poor blood would be about the same as the arterial blood, but the cell-rich blood would have a much higher vis- cosity than arterial blood because of the relationship of the cell concentration to the viscosity of blood _(Bay1ess, 1952). Trueta (19h?) previously had postu- lated the existance of these “shunts" in the rabbit kidney. The cell separation hypothesis has been widely argued and mainly discredited rather than confirmed. There can be no doubt that some plasma skimming occurs in the kidney. However, as Haddy (1958) points out, the possible increase in viscosity could not account for the changes necessary to explain autoregulation. Seriously questioning Pappenheimer's theory, Thompson (1957) found that autoregulation occurred to the same degree in normal and anemic animals. Weiss (1959) was able to obtain autoregulation in the isolated rat kidney in the absence of red cells (perfusion with cell-free dextran). He concluded that autoregulation involves a physiological mechanism rather than a cell separation mechanism. After the beginning of the author's experiments, another theory was advanced by Hinshaw (1959b, 1959c, 1960). He submitted that the increase in resistance is caused by an increase in the extravascular pressure within Bowman's Capsule. The mechanism of ”critical closing" (Nichol 2£_§l,, 1951) may also be involved in the control of circulation in the kidney. In the kidney and many other vascular beds, there must be a certain finite pressure difference across the bed before blood flow through the bed will start. Conversely, flow will cease while there is still a positive pressure of 5-20 mm.Hg . The concept of critical closing is based upon the equations of LaPlace as developed for the soap bubble. If the cross section of a blood vessel wall is thought of as concentric rings, this analogy will apply. It states that the tension in the wall of the vessel is equal to the product of the transmural pressure and the radius. If the pressure is dropped from some equil- brium value, it will eventually reach a point where no equilibrium can be maintained between the tension and radius and the vessel will collapse. Hinshaw (1959a) found, however, that in the kidney, the closing pressure was related to the tissue pressure and no concept of critical closing was needed to explain the phenomenon of closure of the vessels. As a starting point, it was considered that a unified explanation for the control of distension, the mechanism of autoregulation, and the characteristic closure of vessels of the kidney was necessary before the problem of the relation of distension to hyper- tension could be investigated. In order to gain infor- mation concerning these control mechanisms, an analysis of the physical forces involved in the kidney dynamics was made by measuring renal arterial and venous pressure, renal blood flow, and weight of the kidney. MATERIALS AND METHODS The experimental animals used were mongrel dogs, ranging from fifteen to twenty-five Kg., with the mean weight being about twenty Kg. The dogs ranged in age from six months to twelve years and were divided into four groups: (1) immature, (2) young adults, (3) old adults, and (h) senile, with two to four dogs per group. The left kidney was exposed by a flank approach and all tissue connected to the kidney doubly ligated and sectioned between ligatures to prevent capsular bleeding. Great care was taken not to occlude the renal artery or vein so that the kidney would neither become ischemic nor distend abnormally. Before removal of the kidney, the ureter was cannulated with a polyethylene cannula of the largest size possible, in order not to increase tubular pressure, and the urine was allowed to flow during the remainder of the procedure. After the perirenal fat was separated from the kidney and the artery and vein were dissected free for cannulation, the kidney was allowed to return to its normal position for 20 minutes so that it might recover from the stress of manipulation. During this period, the femoral artery and veins were prepared for cannulation. The dog was then given 2 mg/Kg of sodium heparin to prevent clotting and both femoral veins and one femoral artery were cannulated. The femoral artery cannula was led to a polyethylene feed-through connector on the side of a kidney perfusion chamber. The renal artery and vein were then doubly clamped with hemostats near the aorta and vena cava and sectioned between the hemostats. The artery was clamped first so that the kidney would not distend abnormally. The kidney was then removed from the dog and the artery and vein were cannulated with blood-filled, heparinized, polished stainless steel cannulae, (E) (refer to Figure l for placement of components), which were selected because of their known resistance after the ligature had been tied to hold them in place. After the kidney was placed in a supporting basket, the basket was hung from a transducer (G) connection inside the perfusion chamber and the arterial and venous cannulae were connected to the inside of the feed- through connectors (M). The venous connector had been previously attached to a length of Tygon tubing which ended in an adjustable reservoir (I). This reservoir was emptied by means of a Sigmamotor Pump (Model T-6) (J) and the blood returned to a reservoir (K) which was at a fixed height over the dog (A). The cannulae from the femoral veins (L) were attached to the bottom of the reservoir so that the blood would return to the dog. All tubing in the system was } inch (I.D.) Tygon with the exception of the arterial and venous cannulae which were the largest possible size to fit into the respective vessels. No glass was used in the system in order to minimize likelihood of clot formation. Uhen the cannulae were in place, a clamp on the arterial cannula was released and blood flow was allowed to commence. The average ischemic time for the kidney was approximately hi minutes. There were no detrimental effects from keeping the kidney ischemic up to 10 minutes at 20° C. Figure 1 illustrates the perfusion appartus. The perfusion chamber was used so that the kidney could be maintained at 38° c. and 100% humidity. If the kidney cools and the capsule dries, the resistance to flow will increase abnormally, and distensibility will be reduced. The chamber also provided connection points for the cannulae and support for the transducers. With the above perfusion system, flow (Q), venous pressure (Pv)9 arterial pressure (Pa), and the weight of the kidney could be measured readily. The weight of the kidney was measured by suspending it from a Statham strain gage, Model GI-32-h50, which was mounted from the top of the perfusion chamber. This strain gage had a maximum load capacity of almost 1 Kg. and a sensitivity of a few milligrams. The Brush Uni- versal Strain Analyzer was used as a bridge balancing amplifier and power source for the weighing strain gage. The output of the Brush Analyzer was read on one channel .a CLJmmuw .._lIIl.! 10 of a Sanborn Poly-Vise Recorder, Model 67—1200. The gage was calibrated directly by adding weights to the basket on which the kidney was to be suspended and the calibration was constantly checked throughout the ex- periment by electronic means. The distension (D) is the per cent increase in weight of the kidney above the drained weight. Drained weight is the weight of the kidney after draining to equilibrium during arterial stasis and with zero venous pressure. Blood flow in this study was measured by timing the volume outflow from the venous reservoir. This method will only measure the average flow over a 15- 30 second period. Because in certain instances of rapidly changing resistance, the transient flow changes are important, an electromagnetic flow meter should be constructed after the design of Richardson (1959) or something similar. Arterial and venous pressures were measured with a Statham transducer (P23A) or Sanborn Model 2678 Differential Pressure Transducer for arterial measure- ment and Statham P23BB for venous measurement. The transducers were controlled by Sanborn carrier amplifiers. Weight of the kidney, arterial pressure and venous pressure were displayed on a Sanborn h-channel polygraph and monitored with a Sanborn Viso- Scope Unit. Both of the transducers were fixed in place on the 11 end of the perfusion chamber next to the feed-through tubes so that their diaphragms were level with the axis of the kidney. The perfusion chamber was equipped with clamps so that the transducers were always placed in the same position. Short, large polyethylene Y-tubes (C) formed the liquid junction between the transducers (D, H) and the perfusion system in order to reduce the damping to a minimum. The arterial pressure at the kidney could be varied from 25 to 1&0 mm.Hg by raising and lowering the dog which was located on an adjustable platform. This was done so that the arterial pressure could be changed throughout a sufficient range by adding or subtracting a hydrostatic pressure. The use of drugs to change the blood pressure of the dog was objectionable because of their effect on the vascular bed of the kidney. The system of reservoirs Open to the atmosphere, namely, the adjustable reservoir (I), and the femoral reservoir (K), was necessary in order to locate exactly any resistance changes in the system. For example, venous pressure in the system was determined by the resistance of the Tygon tubing leading from the kidney to the variable reservoir divided by the flow plus the hydrostatic head. Because resistance of the tubing was very small, the venous pressure would not change appreciably with flow and, therefore, could be controlled under all conditions. If the 12 cannula from the kidney ran directly to the femoral vein of the dog, the venous pressure would equal the resistance of the tube divided by the flow plus the hydrostatic head plus the venous pressure in the dog. The latter was not controlled. The arrangement used, therefore, removed the influence of the animal's venous pressure. 13 CALCULATIONS Calculation of resistance to flow has been con- troversial because in a vascular bed there exists a "yield pressure". This is a pressure ranging from 6 to 20 mm.Hg which is necessary to initiate flow. In renal blood vessels, even though the resistance is non-linear (autoregulation), Poiseuille's Law applies under any given condition of pressure and flow (Burton, 1952). Q _ (Pa-Pv)rqfl' (l) — n L 8 The usual usage of resistance to flow is that of ohmic resistance which may be written: (Pa-Pv) 8 L R =m= k Q “;£;—' (2) This is analagous to resistance to current in elect- rical circuits. Carlill (1958) suggests that the first derivative 3123.21 (dynamic resistance) be (Pa-Pv) used to replace the ohmic resistance ____.__. He Q points out that when the pressure-flow plot is recti- linear,.% will decrease rapidly with an increase in pressure. He further asserts that if the pressure- flow plot is rectilinear, then the resistance must be a constant so the use of.£ , as an expression of resistance is, therefore, not valid. As Burton (1958) pointed out, however, gglhas no relation to the size 1h of the vessel lumen and therefore should be used only where the rate of change of flow in a vascular bed with the change in blood pressure is importants u .Ei (l) i=23=11L+£d +Pr“di (3) R dP 8 rkl. q dP 1. dP In the present study, where the control of cir- culation was important, analyses were made using "dynamic resistance" .gg . However, when the value of the resistance to flow was important, the Standard ohmic resistance was used. When referring to re- sistance to flow, the "dynamic resistance" will be used and denoted a R’ and the ohmic resistance will be denoted as R. Distensibility (.8) of the kidney is defined as 32—-; that is, the change in distension with respect de to the change in distending pressure. The distending pressure is defined as that pressure responsible for the distension of the kidney. On an anatomical basis and with eXperimental data concerning the permeability of the different vessels of the kidney (Collings, 1958), it was concluded that the distending pressure is the average pressure in the peritubular capillary bed. In order to measure distensibility, the renal artery was clamped and venous hydrostatic pressure was raised. In this static condition, pressure throughout the kidney was the same. Therefore, the venous hydrostatic head 15 was equal to the distending pressure. In this manner, distensibility can be calculated. It was found that distensibility remained constant throughout the period of our experiment. By measuring distension of the kidney, after blood flow was resumed, the pressure needed to produce this distension (Pd) could be calculated. 16 RESULTS AND DISCUSSION DISTENSIBILITY Using the procedures described in the section on "Methods" above, the following kinds of data were obtained: (1) kidney weight, (2) renal arterial and venous pressures, and (3) blood flow rate through the kidney. Data from these measurements are in Appendix A. Resistance, distension, and distensibility were calculated from the above data by procedures outlined in the section on "Calculations”. With two exceptions, plots of were found to have El“ three phases (Figure 2). The first phase has a greater distensibility (slope) than the second phase which has a distensibility greater than that of the third phase. The distensibility of the first phase was interpreted as being associated with filling of the vascular tree, while the distensibility of the second phase was associated with filling of the available interstitial space. The slepe of the third phase was the disten- sibility of the capsule which had to be stretched after available Spaces of the kidney were filled. Kidney 11-25-59 did not show these phases because the Pd was not increased to the range in which the third slope is encountered. Kidney 12-17-59 was a single spontaneous hypertensive animal studied which is discussed below. The data for Figure 2 are incorporated 1? Said. cheats. oeualnl. . 5-3.87 .4..... )0“ 18 in the data tables in the appendix. The relationship between distension (D) and the distending pressure (Pd) as shown in Figure 2 were obtained by procedures out- lined in the section on "Calculations”. The distensi- bility'(i8) is defined as the slopeigga of the ga»curves. This has three distinct valued which are referred to as S. , §x , and.183, corresponding to the first, second, and third slope. Another analysis of these forces was done by analyzing the response of a drained kidney to a single step increase in arterial pressure. The typical response is shown below (Figure 3). Figure 3a. 19 The record (below) shows the weight change of a kidney subjected to a single step increase in arterial pressure (above). Figure 3b. The relationship of distension to time appears to be an exponential function in four phases (Figure A). Kt The expression then becomes‘%— = ae . The quantity 0 (K) will determine the slape of the logD vs (t) plot and is inversely proportional to "resistance to filling". "Resistance to filling" is a composite resistance. Among the factors associated with resistance to filling are: (1) afferent resistance to flow, (2) pressure which tension of the capsule is exerting on incoming blood, and (3) hydrostatic pressure of the fluids within 20 37 26 Log 5.6 o . 200 T(sec) #00 Figure A. 21 the kidney. Each compartment of the kidney has a different resistance to filling. For example, it is easier to fill the vascular tree than to stretch the kidney capsule. Therefore, the slope will change as each compartment is filled and a greater resistance to filling is encountered. As one might expect, the points of change of slope of the«l2%—2 relationship occur at the same distension as the points of change of slope of the %— relationship (Figure 2), which (I also depend on the resistance to filling. The distension at which the slope of the curve .l2§_2 and.2_ plots should, then, 1: Pd approximate the volumes of the compartments being changes in the filled. This is supported by work on determination of the size of the vascular tree by Weaver (1956) by injecting latex and by Collings and Swann (1958) on the size of the vascular and interstitial compartments with a tracer technique which show the volumes of the spaces to be in the same range as those determined by Table 1 gives the relationships between disten— sibility and age. In this table, 8, (which is the slope of the first phase of thelgz relationship, Figure 2), represents resistance to filling of the vascular tree. There is no correlation between age and 8‘ because the value of 8' depends on the state of the kidney prior to filling. For example, the 22 amount of sympathetic tone will determine the resis- tance of the afferent arterioles and the amount of collapse of the venous side of the circulation will depend on pressure relationships while draining. 31_(which is the slope of the second phase (Figure 2» represents the distensibility of the interstitial space, and seems to be correlated with age. The third phase, <$3 (which is the sloPe of the third phase), is the distensibility of the capsule. With the exception of one kidney, 1-16-60, the logarithm of the $3 is preportional to the age of the dog. Figure 5 is a graphical representation of the relationship. One spontaneous hypertensive animal (12-17-59) was studied. The systolic femoral pressure under sodium penobarbital anesthesia was over 200 mm.Hg. The kidney from this dog showed a very low 33 and an interstitial compartment volume of less than 1% of the drained kidney volume which is about 1/15 of the interstitial volume of a normal kidney. These results are compatible with the conclusions of Swann (1959) whose theory states that a diminution of the interstitial volume is responsible for hypertension. 23 Table 1. RELATIONSHIPS BETWEEN DISTENSIBILITY AND AGE Dog Age 8. 8, 8.3 12-17-59 10 yrs* 0.358 0.111 0.111 12-16-59 12 yrs 1.67 0.312 0.200 11-25-59 10 yrs 2.hh 0.375 not taken 12-18-59 a yrs 2.12 0.600 0.29u 1-23-60 3 yrs 1.10 0.800 0.300 1-16-60 2% yrs 1.30 0.930 0.62 12—20-59 5 mos 2.uu 1.300 0.35 The data in Table 1 were obtained by measuring the slopes of the first, second, and third phases in Figure 2. These slopes correspond to 3. , 8, ,1and 53 respectively. 2h .h .2 2 6 10 Age in Years Figure 5. Figure 5 shows the relationship between the distensibility of the capsule (53) and the age of the dog. 83 is defined as the slope of the third phase of the D-Pd relationship in Figure 2. The age of the dogs was determined by a veterinarian by noting the dental wear. (The author is indebted to Dr. Raymond Johnston for his help.) 25 STUDIES ON A MODEL OF VENOUS RESISTANCE A study was made in this laboratory (Wells, 1960) on the nature of the resistance which is responsible for the increase in resistance in autoregulation. Wells found that the resistance was located in the section of the kidney distal to the peritubular capillaries. He also found that this resistance was responsible for the maintenance of distension because an increase in a resistance distal to the peritubular capillaries would increase the average distending pressure. Based upon the foregoing clue, a model was con- structed in an effort to analyze the pressure relation- ships necessary for a change in this venous resistance. Figure 6 diagrammatically represents the model. nb—————-driving pressure collapsing / pressure [Ava/\/Vflv4/\/\/\c’V/t/V’\/V4::::}__s W/VVW I collapsible tube T“— Figure 6. 26 The resistance of the collapsible tube increases with an increase in collapsing pressure, even though the transmural pressure may be increased. The transmural pressure is defined as the difference between the pressure inside the vessel and the opposing pressure outside the vessel. Figure 7 shows the relationship of the driving pressure to the flow. In Figure 7a, the collapsing pressure is 22 cm. of water and in Figure 7b, the collapsing pressure is 30 cm. of water. Figure 8 shows this same relationship plotted on semi-log paper. Figure 8 gives the relationship of closing pressure to collapsing pressure and shows that a change in collapsing pressure gives a change in resistance «3- . At this time, there is no complete explanation offered for this phenomenon. The equations relating pressure to flow derived from the model show an exponential relationship: Bit I KP or P = PoeKQ (h) 27- P (Driving) n 7 gure a. onefizo 50 25 collapsing pressurgfl_,____ 0 cc/m1n. 100 200 L900 Q, P (Driving) CMeHZO 50 Figure 7b. collapsing_pressure ‘__ 25 0 cc/min. 100 200 Figure 7. 28 80 Leg 0051120 1&0 20 10 (Driving) cc/min. 100 Figure 8. 29 200 D This relationship also holds true for the resistance change of the kidney. The typical rela- tionship in an autoregulating kidney is shown in Figure 9. mm.Hg 200 100 0 cc/min. 100 Figure 9. 30 Figure 9 is a graph of the pressure drop across the kidney (Pa‘Pv) against the blood flow (Q). The data for this relationship are to be found in the appendix. The original data were obtained by prodecures outlined in ”Methods". Plotting this on semi-log paper shows the exponential relationship (Figure 10). f 1 80 10 cc/min. 20 0 80 100 Figure 10. 31 Selkurt (19h6) found the same exponential relation- ship. Holt (1959) clarified many of the problems of fluid flow through collapsible tubing. He first found that Poiseuille's equations modified for eliptical tubes could be applied to collapsed tubing: )1 (hlpg-thg) a3b2 lvqi. a2+b2 Q = (5) In the horizontal tube, only the down-stream end is collapsed and the equation becomes: 77(P1-P2) a3b2 Q = UrLL :3:;5 (6) The flow in collapsible tubing differs from that in rigid or in elastic tubing. In rigid tubing, the cross sectional area remains fixed regardless of the transmural pressure. In elastic tubes, the cross sectional area varies with the transmural pressure. However, in collapsible tubes, the lateral pressure down the length of the tube is zero and does not change with flow. Also, the cross sectional area of the tube and the mean velocity of flow increases as the flow increases. Holt further states that when the flow is small, the lateral pressure at the ends of a vertical tube will be different from zero because the tube is partially elastic and a certain finite pressure is needed to maintain the deformation of the tube. 32 Applying Bernoullis' theorem, modified for a viscous liquid, to collapsible tubes (Ference, 1956): AMg(h1-h2) + PlAllet - P2A2v2At (7) = gamvlz-vzz) + ’rLAM where: 45M gm. of liquid enters and leaves the tubes in time A t. Pl, A1, and hl are the lateral pressure, cross sectional area, and relative vertical height at one end and P2, A2, and hz are correSponding values at the other end. v is velocity of flow. fi‘is the heat energy per unit mass, per unit length, lost by the liquid. L is the length of the tube between A1 and A2. g is the acceleration due to gravity. Since the cross section, lateral pressure and velocity are the same for the length of the tube, this expression becomes (Holt, 1959): AMg(h1-h2) = TLAM (8) Holt also found that as a tube starts to collapse, it pulsates and as it becomes more collapsed, the pulsation rate increases until the tube is fully collapsed and the pulsation ceases. In the kidney studies presented here, when the renal venous pressure was zero or slightly negative and other conditions were controlled very carefully, the 33 venous pressure could be made to pulsate in this manner (Figure 11). It was found further, that if the tempera- ture of the kidney was altered 0.50 C. and all other conditions held constant, the pulsation would disappear. With the same collapsible tube model, it was found that the closing pressure (pressure gradient with zero flow) was within one cm. of water of the applied collapsing pressure. This is compatible with the results obtained by Hinshaw (1959a), who found that after occlu- sion of the renal artery the arteriovenous pressure difference fell to a mean of 2.9 mm.Hg. He suggested that the existing renal tissue pressure acts as a collapsing force on the renal blood vessels. Burton (1951) stated that the closing pressure can be used as an index of vasomotor tone in the vessel. For a given active tension, there is then what may be called a ”critical closing pressure”. The greater the active tension, the higher will be the critical closing pressure. He, however, considers the tissue (inter- stitial) pressure to be zero, or nearly zero. In the case of the kidney and other organs, the tissue pressure may rise to values of 25-60 mm.Hg (Montgomery, 1950; Gottschalk, 1956; Hinshaw, 1959a) and would, therefore contribute to the closing of the vessels. A concept of a "veno-vasomotor reflex" has been set forth by Burton (1956) and Rosenberg (1956). They 3h A‘SIUXI‘MII 1‘!"I.3Eh ‘II 1|II“. 'Ir. II!O.C- IICI'I.‘.UeELII Uh.‘.fln DC lufi‘ll. .0 a e L L H U 1 i a. ~ I I U ' I. Ice-0.4.37! wilt'EI .0.»1 f1. 1 a «.elwbtxeiwsnlfllls mnltlit' lJ-u.lasv .39.... C E I. Itlflls. stands-one: v w...flLtfl£v.—Iru itlurU' Ibnnfl-Il Figure 11. Figure 11 shows the pulsation of the venous pressure (Pv)' 35 found that a higher closing pressure was elicited by the distension of the venous side of a vascular bed. They interpreted this as an increase in a vasomotor tone of the arterioles. However, as shown by the work of Gottschalk, (1956), and the author, the peritubular capillary pressure will increase markedly with a rise in the venous pressure. This results in an increase in the average peritubular capillary pressure and will therefore increase tissue pressure. The increase in interstitial pressure will then cause a greater closing pressure. Hinshaw (1959a) measured tissue pressure in the kidney and his work bears out these facts. The active tension in the wall of the vessel would also contribute to the closing phenomenon, however, in such areas as the kidney, the high interstitial pressure would most certainly be the controlling factor. Nichol (1951) has shown that the level of the closing pressure and the resistance to flow at higher pressures are closely correlated in the rabbit ear. They attribute this to the "vasomotor tone". However, it has been demonstrated in the present work, that this is more likely a function of tissue pressure. 36 SUMMARY AND CONCLUSIONS 1. Methods are described by which the distending pressure in the kidney may be found and the disten- sibility of the capsule calculated. 2. Distensibility of the kidney is linear and decreases as the vascular and interstitial compart- ments of the kidney are filled. 3. Distensibility of the capsule appears to be in- versely pr0portional logarithmically to age of the dog. A. One spontaneous hypertensive animal studied had a low capsular distensibility and a small interstitial volume. 5. The mechanism of change in resistance in auto- regulation was found to similar to the collapsing of thin-walled tubes in a physical model. 6. It is suggested that kidney tissue pressure is responsible for closure of the vessels and increase in resistance following venous distension. 37 APPENDIX A 38 Table 2. STATIC WEIGHT AND DISTENDING PRESSURE MEASUREMENTS Pd ... ng.* D%** Pd ng. D% Dog ll-eré9 Kidney_wt_52gm Dgg 12-17-59 Kidney wt 6232 1.0 2.5 ”.5 “.0 1.0 1.6 2.0 0.0 7.0 10.0 3.0 5.0 3.0 5.5 9.5 30.0 4.5 7.0 “.5 7.9 13.0 39.0 5.0 8.0 12.0 9.5 16.0 “7.5 5.0 8.0 .19.0 10.5 18.5 57.0 6.0 9.5 6u.0 7.0 11.0 Dog_12-16:59 Kidney wt 85gm Dgg 12-18-59 Kidney wt 58gm 0.0 2.0 2.3 8.0 11.0 19.0 3.5 7.0 8.2 22.0 16.0 28.0 8.0 13.0 15.3 30.0 17.0 29.5 16.0 16.0 19.0 38.0 18.2 31.5 25.0 18.7 22.0 “6.0 19.5 34.0 33.0 21.0 25.0 72.0 22.5 39.0 02.0 23.0 27.0 5h.0 25.0 29.5 59.0 26.0 30.5 72.0 28.0 33.0 8U.0 29.0 3u.0 * ng = the increase in weight due to the distending pressure. ** D% = per cent increase in weight *“ Pd 8 distending pressure in unoHB 39 Pd Table 2. ng. 10.0 15.5 2500 29.0 31.0 32.0 33.0 35.0 37.0 39°C 0% lbo3 22.2 3600 [41105 “3.5 h6.0 h7.2 50.0 53°C 55-8 (Continued) Dog 12-20-59 Kidney wt 7ng Kidney wt_73.hgm 109 908 12.6 1h.0 18.5 20.0 21.0 25.0 28.5 32.5 35.h 2.6 1305 17.2 19.0 25.3 27.2 28.9 3ho5 39°C 00.5 h8.1 b0 Pd 3.0 10.0 1900 27.0 35.0 “3.0 50.0 58.0 ng o D% Dog l-23:60 Kidney wt Sggg 205 11.2 18.7 2h.5 26.3 28.7 30.0 33.8 Table 3. PRESSURE, FLOW, AND WEIGHT MEASUREMENTS WITH CALCULATED DISTENDING PRESSURE AND RESISTANCE Dog Pa :1: Pv Q n: D Pd Rk 11-25-59 02 2.0 56 6.6 2.0 0.715 07 2.0 70 6.2 2.0 0.603 53 2.0 70 7.9 2.3 0.690 63 2.0 70 9.7 3.2 0.800 68 2.0 76 11.5 3.8 0.870 72 2.0 72 12.0 0.0 0.970 72 6.5 66 16.0 12.0 0.985 67 10.0 00 21.0 25.5 1.32 56 20.0 32 25.5 37.0 1.12 12-16-52 65 3.0 106 19.0 0.585 81 3.0 120 21.0 0.600 87 3.0 120 23.5 0.700 01 2.3 70 13.0 0.560 62 2.8 100 16.5 0.590 67 9.0 78 19.5 0.705 77 9.0 118 20.5 0.575 83 9.5 120 25.0 0.613 60 9.2 100 23.5 0.090 68 19.0 80 25.0 0.613 82 20.0 110 28.0 0.575 12-12-52 85 0.0 57 5.0 1.09 88 0.0 63 5.0 1.00 113 0.0 72 5.0 1.07 118 0.0 80 6.0 1.08 115 0.0 85 6.0 1.35 113 1.0 86 6.0 1.32 12-18-52 00 0.0 00 19.0 1.00 60 0.0 52 20.0 16.0 1.07 70 0.0 60 25.0 18.0 1.10 85 0.0 69 27.5 21.5 1.17 98 0.0 72 29.5 29.0 1.30 98 0.0 75 30.0 31.0 1.25 * 8 all pressures in mm.Hg ‘* I flow in cc/min. 01 Dog 12-20- 1-16-60 1-23-60 9 Table 3. [Np-eh. 00000000 000000000 H 0 III \O\O\O FWOI-‘OCAOQOO 00 00°00 OOOOOOOOO llllll \O\O\O\O\O\O 0 o o o 0 o 0 00000000 WWC’WUUNN (Continued) 06 05 00 00 60 50 80 70 70 50. 80 102 106 128 z 120 160 100 128 100 108 128 136 150 168 180 200 02 1300 27.0 30.5 38.5 23.5 29.0 39.5 01.5 03.0 13.5 17.1 20.0 20.0 37.2 37.2 00.7 00.7 00.7 30.0 35.0 3701'; 00.0 02.5 05.0 50.0 52.5 I-bI-et-A uwmmmooouot: "U occoooooe Q. \JOF'NOUIOOUI HHH p—s O O o 10.0 NN UU \JIUIUIUI 43'? UK.) 09.0 c- \o o 09.0 8.0 13.0 16.0 19.2 22.0 25.5 03.0 50.0 1.37 1.17 1017 1009 0.985 1.06 0.700 0.770 0.770 0.780 0.650 0°59? 0.575 0.600 0.680 0.605 0.675 0.755 0.635 0.622 0.600 0.670 0.652 0.600 0.622 0.590 t(sec) WEIGHT AND TIME MEASUREMENTS ngo Dog,12-18:52 0 12 16 20 20 28 32 36 00 100 160 200 300 000 500 Table 0. D93 20.5 03 t(sec) ngo 29211-25-52 11.5 12.0 11.5 00 NmUUli-‘NOVQO O O O O H UWF'FUthVmO O Table 5. PRESSURE AND FLOW MEASUREMENT FOR PHYSICAL MODEL a b Closing Pressure=22cm water Closing Pressure-30cm water P Q P Q cm water cc/min. cm water cc/min. '20 0.6 20 0.0 21 5.0 25 0.0 22 8.8 29.8 0.0 23 11.0 32.7 16.7 20 18.0 36 80.0 25 26.6 38 106.0 26 08.0 00 116.0 28 72.0 02 136.0 31 103.0 05.8 171.0 30.5 150.0 50 225.0 00 212.0 60 300.0 05 250.0 02 168.0 50 300.0 00 150.0 60 000.0 39 138.0 50 327.0 38 123.0 00 250.0 36 106.0 35 200.0 35 92.0 30 107.0 30 76.0 25 80.0 33 67.0 23 06.0 32 51.0 22 30.0 31 33.0 21 13.0 30 30.0 29.5 11.5 00 APPENDIX B 05 Pressures Pa - Pv - Pd - TABLE or SYMBOLS Arterial pressure at the kidney Venous pressure at the kidney Pressure responsible for the distension of the kidney = mean peritubular capillary pressure Pressure drop across total resistance of kidney Pressure droP from the mean peritubular capillary pressure to the venous pressure Transmural pressure = intravascular pressure - extravascular pressure Total renal resistance Resistance of the portion of the kidney between the peritubular capillary bed and the site of venous pressure measurement Resistance of the portion of the kidney from the site of arterial measurement to the peritubular capillary bed. 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