Renal corpuscular hydrodynamics: Digital computer simulation

Summary A mathematical model of the renal corpuscle is presented and used to quantify the effect on filtration rate, nephron blood flow and hydrostatic pressure in the glomerular capillaries of variations in: 1. the hydrostatic pressure in Bowman's space; 2. the hydrodynamic resistances of the afferent and efferent arterioles; 3. the ultrafiltration coefficient of the glomerular membrane; 4. the hydrostatic pressure in the peritubular capillaries; 5. the arterial haematocrit and plasma protein concentration. The model is derived from the principle of conservation of mass and volume. Hydrostatic pressure gradients along the glomerular capillaries are neglectec. The hydrodynamic resistances of the afferent and efferent arterioles are assumed to be determined by two independent factors, one being determined by the vascular dimensions, the other by the haematocrit. Blood flow is considered to be related in a linear manner to the hydrostatic pressure decreases along these vessels. The effect of changing the hydrostatic pressure in Bowman's space on nephronGFR was calculated and found to agree with experimental measurements. When corpuscular hydrodynamics are related to variations in the hydrodynamic resistance of the afferent or efferent arteriole it is seen that the change in efferent arteriolar plasma flow accompanying altered nephronGFR is very sensitive to the way in which the change is produced. In contrast changes in glomerular capillary pressure and filtration fraction are insensitive. The calculations indicate that differences measured in nephronGFR between superficial and juxtamedullary nephrons can be explained by assuming that the diameters of the afferent and efferent arterioles of the juxtamedullary nephrons increase in direct proportion to the diameter of the renal corpuscle.     

Maturational development of glomerular ultrafiltration in the rat.

To ascertain the cause of low glomerular filtration rate in newborn and immature mammals, we measured glomerular pressures and flows directly in immature (30- to 45-day-old) euvolemic Munich-Wistar rats with surface glomeruli. As with total kidney GFR, single nephron (SN)GFR was found to be significantly lower than in adult rats, on average by 40% when corrected for kidney weight. Equality between efferent oncotic pressure and transglomeruler hydraulic pressure difference (deltaP) was usually achieved in immature rats, indicating that the glomerular capillary ultrafiltration coefficient is not a factor limiting SNGFR and GFR in immature rats. Although the average values for deltaP in immature rats were slightly, albeit significantly, lower than in adults, markedly lower values (79 +/- 5 vs. 136 +/- 10 nl/min per g kidney wt) for glomerular plasma flow rate (QA) proved to be the primary factor responsible for the lower SNGFR and GFR values in immature rats. Considerably higher values for afferent and efferent arteriolar resistances contributed to this low QA state in immature rats.     

Angiotensin II and renal prostaglandin release in the dog. Interactions in controlling renal blood flow and glomerular filtration rate

The relationship between angiotensin II and renal prostaglandins, and their interactions in controlling renal blood flow (RBF) and glomerular filtration rate (GFR) were investigated in 18 anaesthetized dogs with acutely denervated kidneys. Intrarenal angiotensin II infusion increased renal PGE₂ release (veno-arterial concentration difference times renal plasma flow) from 1.7 ± 0.9 to 9.1 ±0.4 and 6-keto-PGFja release from 0.1 ±0.1 to 5.3 ± 2.1 pmol min^-1. An angiotensin II induced reduction in RBF of 20% did not measurably change GFR whereas a 30% reduction reduced GFR by 18 ± 8%. Blockade of prostaglandin synthesis approximately doubled the vasocon-strictory action of angiotensin II, and all reductions in RBF were accompanied by parallel reductions in GFR. When prostaglandin release was stimulated by infusion of arachidonic acid (46.8± 13.3 and 15.9± 5.4 pmol min^-1 for PGE₂, and 6-keto-PGFja, respectively), angiotensin II did not change prostaglandin release, but had similar effects on the relationship between RBF and GFR as during control. In an ureteral occlusion model with stopped glomerular filtration measurements of ureteral pressure and intrarenal venous pressure permitted calculations of afferent and efferent vascular resistances. Until RBF was reduced by 25–30% angiotensin II increased both afferent and efferent resistances almost equally, keeping the ureteral pressure constant. At greater reductions in RBF, afferent resistance increased more than the efferent leading to reductions in ureteral pressure. This pattern was not changed by blockade of prostaglandin synthesis indicating no influence of prostaglandins on the distribution of afferent and efferent vascular resistances during angiotensin II infusion. In this ureteral occlusion model glomerular effects of angiotensin II will not be detected, and it might well be that the shift from an effect predominantly on RBF to a combined effect on both RBF and GFR induced by inhibition of prostaglandin synthesis is located to the glomerulus. We therefore postulate that renal prostaglandins attenuate the effects of angiotensin II on glomerular surface area and the filtration barrier, and not on the afferent arterioles as previously suggested.     

Effect of isotonic volume expansion on glomerular filtration rate and renal hemodynamics in the developing rat kidney

Young rats (20–24 days) and adult rats (4–5 days) were studied during hydropenia and volume expansion with regard to glomerular filtration rate (GFR) and the determinants of GFR. During hydropenia, GFR and renal blood flow (RBF) were significantly lower in younger than in adult rats both in absolute terms and when related to bodyweight. Equivalent degrees of volume expansion (6% of b. wt.) resulted in a much more pronounced increase in GFR and RBF in younger than in older rats. This suggests that the high renal vascular resistance in hydropenic young rats is primarily due to vasoconstriction. The relationship between the filtration rate of superficial nephrons and the total GFR was the same in hydropenic and volume expanded rats in both age groups. The tubular stop flow pressure, the calculated hydrostatic glomerular capillary pressure and ultrafiltration pressure in the afferent part of the glomerular capillaries was slightly lower in hydropenic young rats than in hydropenic adult rats. The pressures did not rise after volume expansion. It is concluded that the marked increase in GFR in volume expanded young rats is mainly due to increased renal plasma flow.     

Kinetics of the Glomerular Ultrafiltration in the Rat Kidney. A Theoretical Study

The glomerular filtration process was evaluated theoretically from micropuncture data obtained from Sprague-Dawley rats. The hydrostatic pressures in the glomerular capillaries and Bowman's space minus the oncotic pressure in systemic plasma gave the net driving force at the proximal end of the glomerular capillary. From the single nephron filtration fraction the mean net driving force over the glomerular membrane was calculated to be 20 mm Hg during normotension, decreasing to 12 mm Hg during a perfusion pressure of 80 mm Hg. The hydraulic permeability for one glomerulus was 0.7-0.8 nl/min. 100g b. wt. mmHg. The pressures at the distal end of the glomerular capillaries were 13 and 6 mm Hg under the above two conditions, indicating non-equilibrium of the filtration process at the end of the glomerular capillary. It was shown that the glomerular filtration rate is mainly influenced by the driving pressures. During hypotension an increased plasma flow dependency was evident. Brenner et al. found a filtration equilibrium and a plasma flow dependent glomerular filtration rate in a mutant Wistar rat strain. The discrepancy between their results and ours is due to the low glomerular plasma flow and hydrostatic pressures in the Wistar rats. It is concluded from our results that both pre- and postglomerular resistances may influence the glomerular filtration rate and glomerular plasma flow independently.     

Kinetics of the glomerular ultrafiltration in the rat kidney. A theoretical study.

The glomerular filtration process was evaluated theoretically from micropuncture data obtained from Sprague-Dawley rats. The hydrostatic pressures in the glomerular capillaries and Bowman's space minus the oncotic pressure in systemic plasma gave the net driving force at the proximal end of the glomerular capillary. From the single nephron filtration fraction the mean net driving force over the glomerular membrane was calculated to be 20 mm Hg during normotension, decreasing to 12 mm Hg during a perfusion pressure of 80 mm Hg. The hydraulic permeability for one glomerulus was 0.7-0.8 nl/min-100 g b.wt. mmHg. The pressures at the distal end of the glomerular capillaries were 13 and 6 mm Hg under the above two conditions, indicating non-equilibrium of the filtration process at the end of the glomerular capillary. It was shown that the glomerular filtration rate is mainly influenced by the driving pressures. During hypotension an increased plasma flow dependency was evident. Brenner et al. found a filtration equilibrium and a plasma flow dependent glomerular filtration rate in a mutant Wistar rat strain. The discrepancy between their results and ours is due to the low glomerular plasma flow and hydrostatic pressures in the Wistar rats. It is concluded from our results that both pre- and postglomerular resistances may influence the glomerular filtration rate and glomerular plasma flow independently.     

Intrarenal blood flow distribution in the desert quail following salt loading.

The total-kidney glomerular filtration rate (GFR) falls when birds are salt loaded. This fall in GFR is caused by glomerular intermittency. The nephrons that stop filtering are small, surface nephrons without loops of Henle. Larger nephrons with loops of Henle in the deeper regions of the kidney continue to filter during salt loading. Microfil casts were made of the renal microvasculature of the desert quail, Lophortyx gambelii, in an attempt to determine at what points intrarenal blood flow is regulated to cause glomerular intermittency. Casts of the renal vasculature were made in quail that were hydrated and in quail that were salt loaded. The results indicate that the small, surface nephrons stop filtering during salt loading because of a vasoconstriction at the level of the afferent arterioles of these nephrons. At the same time, blood flow is maintained to the large nephrons with loops of Henle. Reducing GFR at the expenses of excreting wastes can be viewed as a mechanism to conserve body water during periods of water deprivation.     

Renal autoregulation: evidence for the transmural pressure hypothesis.

Autoregulation of glomerular filtration rate (GFR) was examined during uteral orarterial constriction in anesthetized dogs after renal denervation. GFR was sustaineduntil ureteral pressure greater than 80 mmHg, provided renal arterial pressure exceeded 180 mmHg, but fell at ureteral pressure less than 54 mmHg when arterial pressure averaged 127 plus or minus 5 mmHg; renal blood rose as GFR declined. Ethacrynic acid, saline, or mannitol infusion increased tubular pressure without reducing GFR,but during subsequent ureteral constriction GFR fell at uteral pressure less than 40mmHg. During arterial constriction GFR was maintained at lower arterial pressures in hydropenic than in diuretic dogs. Because of thisdifference in the range of autoregulation, saline infusion increased GFR more in hydropenic than in diuretic dogs except at high arterial pressure. This response to reduced plasma oncotic pressure and the constancy of GFR over a wide range of proximal tubular and arterial pressure indicate constancy of thehydrostatic transmural pressure of glomerular capillaries. Afferent arteriolar resistance is, in addition to a regulation by transmural pressure, perhaps controlled by vascular stretch receptors in the glomeruli.     

Dynamics of glomerular ultrafiltration in Amphiuma means

To study renal function inAmphiuma means, the hydrostatic pressures in vascular and tubular structures and the glomerular filtration rate were determined at different arterial blood pressures. In the arterial blood pressure range studied no evidence of autoregulation of the glomerular capillary pressure or of the hydrostatic pressure gradient over the capillary membrane was found. The glomerular filtration ceases at an arterial blood pressure below 12 cm H₂O. No significant difference between tubular free flow pressure and peritubular capillary pressure was noted. Furthermore, it was found that the glomerular capillary pressure could be estimated by measuring the intratubular stop-flow pressure and arterial colloid osmotic pressure at an arterial pressure above 15 cm H₂O. It was also found possible to measure the glomerular capillary pressure at the very end of the afferent arteriole. The protein concentrations in afferent and efferent arteriolar blood were determined and the colloid osmotic pressures were calculated according to a new formula derived forAmphiuma plasma. The dynamics of glomerular ultrafiltration was evaluated. A filtration equilibrium across the glomerular membrane was reached, since the efferent colloid osmotic pressure was not significantly different from the hydrostatic pressure gradient across the glomerular capillary membrane.     

Renal and nephron hemodynamics in spontaneously hypertensive rats.

Renal and nephron hemodynamics were compared between anesthetized, nondiuretic, spontaneously hypertensive rats (SHR) and Wistar-Kyoto rats (WKY). Although the mean arterial pressure was higher in SHR than in WKY, 158 VS. 114 mmHg, glomerular filtration rate (GFR) and renal blood flow (RBF) were similar in both groups. So were intrarenal hydrostatic pressures, single nephron GFR (SNGFR), and single nephron blood flow (SNBF). Accordingly, the increased renal vascular resistance (RVR) in SHR was due to predominant preglomerular vasoconstriction. In a second group of SHR, SHR-AC, the femoral arterial pressure was reduced acutely to 114 mmHg by means of aortic constriction above the renal arteries. The mean values for GFR, RBF, SNGFR, SNBF, and intrarenal hydrostatic pressures resembled those in SHR, whereas RVR was less in SHR-AC. These autoregulatory adjustments of RVR were again largely limited to the preglomerular vasculature. Efferent arteriolar resistance was similar in all three groups. We conclude that the enhanced RVR in 12-wk-old SHR is primarily a consequence of a physiological, autoregulatory response of afferent arteriolar resistance to the elevated arterial pressure. Further, RVR in SHR is not fixed and constant but responds appropriately to reductions in renal perfusion pressure.     

A mathematical model of fluid transport in the kidney

A mathematical model of the rat kidney is developed from glomerular and tubular submodels. It is assumed that all nephrons are identical, that the hydraulic pressure in the tubules obeys Hagen-Poiseuille's law, that the rate of fluid reabsorption depends on the flow rate of tubular fluid, and that the tubules are distensible. The independent variables of the model are selected to comply with experimental measurements in the hydropenic rat. The model is used to evaluate the mechanism of glomerulotubular balance: changing the mean ultrafiltration pressure in the glomerular capillaries has a substantial influence on glomerular filtration rate (GFR). A change in the rate of fluid reabsorption in the proximal tubules has a strong influence on GFR notwithstanding that the change in GFR is smaller than that in the rate of fluid reabsorption. The calculated values for the hydraulic pressure profile in the tubular system and the interstitial pressure during ureteral obstruction are in close agreement with experimental measurements. Increasing the arterial haematocrit above normal causes a substantial decrease in GFR, whilst reducing it below normal has only a small effect on GFR.     

Ophidian kidney preparation for the measurement of glomerular dynamics in real-time

A new ophidian kidney preparation is described which allows the measurement of glomerular arteriolar diameters, glomerular blood flow, and glomerular capillary pressure in real time. Intravital epifluorescence video microscopy is utilized to observe and record blood flow in the renal microcirculation in the garter snake, Thamnophis sirtalis. Carotid, renal artery and glomerular capillary pressures are recorded digitally on the video recording simultaneously with the images with an eight-channel video data recorder, maintaining synchrony of all data. On the video replay, glomerular arteriolar diameters are measured with a video micrometer and RBC velocity determined with the video dual-slit method. Blood flow is continuously calculated from the diameter and RBC velocity measurements. The continuous and simultaneous measurements of the pressure gradient across the afferent limb of the glomerular circulation, the renal artery to glomerular capillary pressure drop, and the rate of glomerular blood flow allow the continuous calculation of afferent glomerular arteriolar resistance in real time. This is the first demonstration of these capabilities in a vertebrate kidney.     

Role of macula densa neuronal nitric oxide synthase in renal diseases

Macula densa cells have an important role in the regulation of glomerular blood flow and glomerular filtration by its regulation of afferent arteriolar vascular tone. Nitric oxide derived from neuronal nitric oxide synthase (nNOS) in macula densa can dilate afferent arterioles. Macula densa nNOS is important for renin secretion, and its expression is regulated by dietary salt, renal angiotensin II, intracellular pH, and other factors. In salt-sensitive hypertension, nNOS is suppressed, whereas in SHR or in the early phase of diabetes, nNOS is increased in macula densa along with NADPH oxidase, which limits NO bioavailability. Renal damage induced by hypertension, diabetes, and hyperlipidemia could be prevented by enhancement of nNOS in macula densa with ACEI, dipyridamole, α₁-receptor blocker, a low-salt diet, or sodium bicarbonate. Sodium bicarbonate is a safe and clinically available enhancer of nNOS in macula densa that increases glomerular blood flow and prevents the reduction of GFR in radiocontrast nephropathy and chronic renal failure. In conclusion, the enhancement of nNOS in the macula densa can be a promising strategy to prevent reduction of renal function.     

The pressure-flow relationship of different nephron populations in the rat.

The mechanisms behind the autoregulation of the total renal blood flow and the glomerular filtration rate are unclear. In this investigation a modified microsphere technique was applied to measure the blood flow at different depths in the renal cortex during normotensive and hypotensive conditions. No autoregulation was found in the outer cortex while it was well pronounced in the inner one. During similar conditions, glomerular capillary pressure, welling point pressure and intratubular pressure were recorded. By combining these results with the blood flow data, the preglomerular and postglomerular resistances were calculated. It was then found that the preglomerular resistance decreased and the postglomerular resistance increased when the blood pressure was lowered. The results indicate a redistribution of blood flow from the outer parts to the inner parts of the cortex when the blood pressure is decreased. The redistribution of the blood flow might explain the well known linear relationship between the arterial pressure and the urine flow. The single nephron filtration rate of the outermost glomeruli could be calculated and the results seem to indicate a non-equilibrium at the end of the glomerular capillaries.     

Annexin A1 protein attenuates cyclosporine-induced renal hemodynamics changes and macrophage infiltration in rats

Background  

Cyclosporine (CsA) remains an important immunosuppressant for transplantation and for treatment of autoimmune diseases. The most troublesome side effect of CsA is renal injury. Acute CsA-induced nephrotoxicity is characterized by reduced renal blood flow (RBF) and glomerular filtration rate (GFR) due to afferent arteriole vasoconstriction. Annexin A1 (ANXA1) is a potent anti-inflammatory protein with protective effect in renal ischemia/reperfusion injury. Here we study the effects of ANXA1 treatment in an experimental model of acute CsA nephrotoxicity.     

The existence of a tubulo-glomerular feedback mechanism in the Amphiuma nephron

A single nephron tubulo-glomerular feedback control of the glomerular filtration rate, which is known in mammlian animals, could be one way by which amphibians regulate the glomerular filtration rate (GFR). To investigate whether theAmphiuma means shows any sign of a tubuloglomerular feedback control, micropuncture experiments were carried out. Six different series of experiments were performed.In the first series, tubular stop-flow pressure (SFP) was measured during distal tubular perfusion with amphibian Ringer solution at a rate of 10, 25 and 50 nl/min. A significant decrease of SFP was found at the three perfusion rates compared to the controls. In the second group, single nephron glomerular filtration rate (SNGFR) was measured, while the distal tubule was perfused at 10, 25 and 50 nl/min. At a perfusion rate of 10 nl/min the SNGFR did not decrease, whereas at 25 and 50 nl/min it decreased significantly. In the third group the perfusion pipette was located in the proximal tubule and the nephron was perfused at 10, 25 and 50 nl/min, while at the same time the proximal tubular stop-flow pressure was measured. No reduction of SFP was found at a perfusion rate of 10 nl/min, while significant reductions were noted at rates of 25 and 50 nl/min. In the fourth group the SNGFR was measured in the distal tubule beyond the macula densa and in Bowman's space of the same nephron. No significant difference was found. In the fifth group, the glomerular capillary pressure (GCP) was measured before and after blockade of the tubular fluid flow. No significant difference was found between these two measurements.The sixth series deals with the changes occuring at the single nephron level by the tubulo-glomerular feedback control. The single nephron filtration fraction (FF) was determined from efferent arteriolar protein concentration with and without a feedback-induced reduction of the SNGFR. The FF values were not significantly different from one another. From these results and data from the other series, the afferent (R _aff) and efferent (R _eff) arteriolar resistances were calculated.R _eff did not change, whileR _aff increased significantly when a feedback stimulus was applied.These experiments indicate the existence of a tubuloglomerular feedback control which depresses the SNGFR and SFP by contracting the afferent arteriole.     

A multinephron model of renal blood flow autoregulation by tubuloglomerular feedback and myogenic response

Tubuloglomerular feedback implies that a primary increase in arterial pressure, renal blood flow, glomerular filtration and increased flow rate in the distal tubule increase preglomerular resistance and thereby counteract the primary rise in glomerular filtration rate and renal blood flow. Tubuloglomerular feedback has therefore been assumed to play a role in renal autoregulation, i.e., the constancy of renal blood flow and glomerular filtration at varying arterial pressure. In evaluating this hypothesis, the numerous tubular and vascular mechanisms involved have called for mathematical models. Based on a single nephron model we have previously concluded that tubuloglomerular feedback can account for only a small part of blood flow autoregulation. We now present a more realistic multinephron model, consisting of one interlobular artery with an arbitrary number of evenly spaced afferent arterioles. Feedback from the distal tubule was simulated by letting glomerular blood flow exert a positive feedback on preglomerular resistance, in each case requiring compatibility with experimental open-loop responses in the most superficial nephron. The coupling together of 10 nephrons per se impairs autoregulation of renal blood flow compared to that of a single nephron model, but this effect is more than outweighed by greater control resistance in deep arterioles. Some further improvement was obtained by letting the contractile response spread from each afferent arteriole to the nearest interlobular artery segment. Even better autoregulation was provided by spreading of full strength contraction also to the nearest upstream or downstream afferent arteriole, and spread to both caused a renal blood flow autoregulation approaching experimental observations. However, when the spread effect was reduced to 25% of that in each stimulated afferent arteriole, more compatible with recent experimental observations, the autoregulation was greatly impaired. Some additional mechanism seems necessary, and we found that combined myogenic response in interlobular artery and tubuloglomerular feedback regulation of afferent arterioles can mimic experimental pressure-flow curves.     

The renal blood flow and the glomerular filtration rate of anaesthetized dogs during acute changes in plasma sodium concentration.

1. The effects of acute changes in plasma Na concentration (P(Na)) on renal blood flow (RBF) and glomerular filtration rate (GFR) were studied in anaesthetized greyhounds. Saline was infused at a constant rate (0.1 ml. kg(-1) min(-1)) either into a renal artery or into a systemic vein. Plasma Na concentration was altered by varying the Na concentration of the infused saline from 0.154 to 0.077, 0.616 or 1.232 M.2. Blood pressure (B.P.), packed cell volume (PCV), concentration of plasma solids (PS) and the plasma concentration of H(+) and K (P(K)) ions were measured but no attempt was made to contain their fluctuation.3. An infusion of hypertonic saline into a renal artery usually led to an ipsilateral increase in RBF for 5-15 min, followed by a progressive fall. Over-all, mean values of RBF fell with P(Na) throughout the range studied (120-190 m-mole l.(-1)). Glomerular filtration rate rose with P(Na) to reach maximal values at P(Na) levels of 140-160 m-mole l.(-1), but fell thereafter. The combined fall in RBF and GFR, without change in filtration fraction, at P(Na) values above 160 m-mole l.(-1) is consistent with an alteration in afferent arteriolar resistance. The fall in GFR despite a rise in RBF noted when P(Na) was reduced below 140 m-mole l.(-1) requires an additional explanation.4. Renal blood flow was independent of P(K); it was inversely related to [H(+)] and directly related to PS. Glomerular filtration rate was independent of PCV and P(K). It was also inversely related to [H(+)] and directly related to PS up to a value of 6 g 100 g(-1) plasma, after which the relationship was reversed. These results suggest that the renal vascular responses to acute changes in P(Na) may be mediated in part, at least, by concurrent change in PS and [H(+)].     

The effect of two different calcium antagonists on the glomerular haemodynamics in the dog

Kidney function of beagles fed a constant amount of food containing 3 mmol sodium.kgbodywt⁻¹.day⁻¹, and anaesthetized with pentobarbitone was investigated by clearance and micropuncture techniques during an intrarenal infusion of saline or the calcium antagonists verapamil (VER, 4 μg.kgbodywt⁻¹.min⁻¹) or nifedipine (NIF, 0.3 μg.kgbodywt⁻¹.min⁻¹). Neither drug changed the mean arterial pressure. Apart from the natriuresis and diuresis, which were significantly greater with NIF than with VER, the response to both drugs was similar. Increases in renal blood flow (RBF; 17% with VER, 20% with NIF), glomerular filtration rate (GFR; VER: 34%; NIF: 39%) and filtration fraction (VER: 12%; NIF: 14%) were observed; similar values were obtained at the single nephron level. Pressure in glomerular capillaries, measured directly after ablation of a thin layer of cortex corticis, was increased by 11% with VER and 10% with NIF; no changes in proximal tubular and peritubular capillary pressure were seen. The glomerular ultrafiltration coefficient (K_f) did not change with either drug. Total arteriolar resistance was decreased (VER: 20%; NIF: 15%) due to a decrease in afferent resistance (VER: 31%; NIF: 27%) with no corresponding change in efferent resistance. The cause of the lack of responsiveness of the efferent arteriole remains unclear. In conclusion, in acute experiments with intrarenal administration, both drugs increase RBF and GFR by a preferential afferent dilatory mechanism without any change in K_f.