Impacts of nitric oxide and superoxide on renal medullary oxygen transport and urine concentration

Abstract

The goal of this study was to investigate the reciprocal interactions among oxygen (O₂), nitric oxide (NO), and superoxide (O₂⁻) and their effects on medullary oxygenation and urinary output. To accomplish that goal, we developed a detailed mathematical model of solute transport in the renal medulla of the rat kidney. The model represents the radial organization of the renal tubules and vessels, which centers around the vascular bundles in the outer medulla and around clusters of collecting ducts in the inner medulla. Model simulations yield significant radial gradients in interstitial fluid oxygen tension (Po₂) and NO and O₂⁻ concentration in the OM and upper IM. In the deep inner medulla, interstitial fluid concentrations become much more homogeneous, as the radial organization of tubules and vessels is not distinguishable. The model further predicts that due to the nonlinear interactions among O₂, NO, and O₂⁻, the effects of NO and O₂⁻ on sodium transport, osmolality, and medullary oxygenation cannot be gleaned by considering each solute's effect in isolation. An additional simulation suggests that a sufficiently large reduction in tubular transport efficiency may be the key contributing factor, more so than oxidative stress alone, to hypertension-induced medullary hypoxia. Moreover, model predictions suggest that urine Po₂ could serve as a biomarker for medullary hypoxia and a predictor of the risk for hospital-acquired acute kidney injury.

nitric oxide (no) and superoxide (O₂⁻) exert opposite effects on renal vascular and tubular function, and the balance between the two significantly modulates the renal handling of Na⁺. NO promotes natriuresis and diuresis and thus favors reductions in blood pressure; O₂⁻ promotes salt and water retention, which raises blood pressure (8).

In vitro experiments on the rat (5) and bovine (66) kidney have shown a dependence of NO and O₂⁻ production on local oxygen tension (Po₂), but the net effects of these three interacting solutes on medullary transport and function remain unclear. What is clear is that medullary tissue Po₂ is low even though the kidney receives 25% of the cardiac output. The low medullary Po₂ stems primarily from the high metabolic demands of the medullary thick ascending limbs (TALs) of the loops of Henle. As a result, the renal medulla is vulnerable to ischemic and hypoxic injury (8).

In vivo microdialysis studies in the rat have demonstrated that medullary NO production can protect the kidney from large reductions of medullary blood flow and ischemia, even in the face of significantly reduced cortical blood flow (9, 70, 72). The renal protective influence of NO may be attributed to its two key physiological effects: vasodilation, which increases medullary blood flow and O₂ supply, and natriuresis, which reduces O₂ consumption. In contrast, increases in O₂⁻ reduce medullary blood flow and result in antinatriuresis (71). Chronic elevation of medullary O₂⁻ levels can reduce NO bioavailability and raise medullary TAL sodium absorption, resulting in a decrease in sodium excretion, both of which may contribute to the development of hypertension (8, 21, 31, 32, 35).

In light of these issues, a principal goal of this study was to investigate how the interactions between NO and O₂⁻ affect medullary oxygenation and active sodium transport and vice versa. To do this, we developed a highly detailed mathematical model of NO and O₂⁻ steady-state transport in the renal medulla that takes into account its three-dimensional (3D) architecture and examined a range of physiological and pathophysiological conditions.

MODEL DESCRIPTION

Our model is based on previously applied models of the urine-concentrating mechanism and oxygen transport in the rat kidney (15, 25, 26), as well as a rat outer medulla (OM) model of NO and superoxide interactions (13). Our model representation accounts for the 3D architecture of the renal medulla using the “region-based” approach (described further below) developed by Layton and Layton (28) and simulates steady-state solute transport in the renal medulla.

The descending limbs, ascending limbs, and collecting ducts (CDs) are represented by rigid tubes that extend from the corticomedullary boundary at x = 0 to the papillary tip at x = L. Two-thirds of the model loops of Henle are assumed to turn at the OM-inner medulla (IM) boundary, whereas the other one-third turn at all depths of the IM. The model separates blood flow in the vasa recta into two compartments, plasma and red blood cells (RBCs), which are both also represented by rigid tubes along the corticomedullary axis. The vasa recta terminate or originate at all depths of the medulla and are assumed to peel off and supply the capillary plexus.

To represent the 3D architecture of the renal medulla and the resulting preferential interactions among vessels and tubules, the model interstitium is divided into four regions. Each region represents the combination of interstitial spaces, interstitial cells, and capillary plasma flow and is assumed well mixed at a particular medullary depth. Each region also contains an RBC compartment, representing RBCs within capillaries traversing the region. To determine the interactions among tubules and vessels, each tubule or vas rectum is assigned to a certain region (or, potentially, fractions of each tubule or vas rectum are assigned to 2 regions); in this way, vessels and tubules contained in different regions are influenced by different interstitial environments.

The positions of the tubules and vessels within the regions at different medullary depths are shown in Fig. 1. The organization of the OM regions is centered around an innermost region that represents a vascular bundle (R1), which contains long vasa recta that reach into the IM. Most of the TALs are contained in the interbundle regions (R3 and R4), far from the oxygen-supplying descending vasa recta (DVR) (30). Similarly, the organization in the IM is centered around the region (R4) that denotes a cluster of CDs. In the upper 3–3.5 mm of the IM, these CD clusters dominate the structural organization of the medulla, with DVR found distant from those clusters (R1) (46, 47, 48, 49). In the bottom 1.5–2 mm of the IM, CD clusters are no longer distinguishable, and the radial organization of the deep medulla is increasingly homogeneous.

Fig. 1.

Schematic diagram of a cross section through the outer stripe, inner stripe, upper inner medulla (IM), mid-IM, and deep IM, showing interstitial regions (R1, R2, R3, and R4) and relative positions of tubules and vessels. Decimal numbers indicate relative interaction weightings with regions [e.g., in the outer stripe, half of the short descending vasa recta (SDV) lie in R1, and half lie in R2]. CD, collecting duct; LDV, long descending vas rectum; AVRs, populations of ascending vasa recta; SDL/SAL, descending/ascending limbs of short loops of Henle; LDL/LAL, descending/ascending limbs of long loops of Henle. Subscript “S,” “M,” and “L” associated with a LAL denotes limbs that turn with the first mm of the IM (S), within the mid-IM (M), or reach into the deep IM (L). Dotted-line box in deep IM indicates that LDV, LDL, LAL, and CD are weighted evenly between the 4 regions. Tubules, vessels, and interstitium are denoted in blue, red, and pink, respectively.

The model predicts fluid flows in the tubules and vessels, as well as concentrations of NaCl, urea, O₂, NO, O₂⁻, deoxyhemoglobin (Hb), oxyhemoglobin (HbO₂), and nitrosyl-heme (HbNO), in each tubule and vessel, as well as in the interstitium. Model equations are based on transmural transport and conservation of water and solutes. Below we summarize key components of the model that represent generation and consumption of oxygen, NO, and superoxide. Full model equations can be found in Refs. 4, 13, 27.

Generation and consumption of NO.

The rate of NO synthesis in the vascular endothelium and tubular epithelium is dependent on the local O₂ concentration. This dependence of the NO generation rate (G_i,NO) on O₂ is modeled by a Michaelis-Menten relationship:

$$G_{i,\text{NO}}=G_{i,\text{NO}}^{\max }\left[\frac{C_{i,{\text{O}}_2}\left(x\right)}{K_{{\text{O}}_2}^{\text{NO}}+C_{i,{\text{O}}_2}\left(x\right)}\right],$$ (1)

where C_i,O2 is the O₂ concentration in tubule or vessel i, G_i,NO^max is the maximal rate of NO synthesis, and K_O2^NO is the Michaelis constant, taken here to be 50.9 μM (66). The value of G_i,NO^max in the vasa recta is chosen to yield interstitial NO concentrations ∼100 nM, based on experimental findings in the rat (72). The ratios between maximal NO generation rates in the vasa recta and the descending limbs, ascending limbs, and CDs are derived from published measurements in microdissected rat renal segments (67).

As in our previous models of NO transport (12, 13, 69), we consider the following NO consumption reactions: the auto-oxidation of NO (rate V₁), the scavenging of NO by O₂⁻ (rate V₂), the irreversible reaction of NO with HbO₂ to form methemoglobin (rate V₃), and the reversible reaction of NO with Hb to form HbNO (rate V₄). The reaction rates for these processes are

$$V_{i,1}=k_{{\text{O}}_2}{\left(C_{i,\text{NO}}\right)}^2{C}_{i,{\text{O}}_2},$$ (2)

$$V_{i,2}=k_{\text{scav}}{C}_{i,\text{NO}}{C}_{i,{\text{O}}_2^{-}},$$ (3)

$$V_{i,3}=k_{\text{oxy}}{C}_{i,\text{NO}}{C}_{i,{\text{HbO}}_2},$$ (4)

$$V_{i,4}=k_{\text{deoxy}}{C}_{i,\text{NO}}{C}_{i,\text{Hb}}-k_{\text{rev}}{C}_{i,\text{HbNO}}.$$ (5)

Reactions with rates V_i,1 and V_i,2 take place in all compartments, whereas reactions with rates V_i,3 and V_i,4 take place only in the RBCs. The total volumetric rate of NO consumption in tubule or vessel i is thus given by

$$R_{i,\text{NO}}=V_{i,1}+V_{i,2}+V_{i,3}+V_{i,4}.$$ (6)

The steady-state conservation equation for NO in tubule i is given by

$$\frac{\partial F_{i,\text{NO}}\left(x\right)}{\partial x}=J_{i,\text{NO}}\left(x\right)+\theta A_i^{\text{epi}}\left(x\right)\left[G_{i,\text{NO}}\left(x\right)-R_{i,\text{NO}}^{\text{epi}}\left(x\right)\right]-A_i^{\text{lum}}\left(x\right)R_{i,\text{NO}}^{\text{lum}}\left(x\right),$$ (7)

where x is the position along the medulla; F_i,NO(x) is the flow rate of NO in tubule i; J_i,NO is the transmural flux of NO into tubule i; A_i^lum and A_i^epi are the cross-sectional areas of the lumen of tubule i and that of the surrounding epithelium, respectively; R_i,NO^lum and R_i,NO^epi are the volumetric consumption rates of NO in the lumen of tubule i and that of the surrounding epithelium, respectively; G_i,NO is the epithelial volumetric generation rate of NO; and θ is the fraction of the amount of NO generated in epithelia that diffuses toward the lumen [with the remainder (1 − θ) diffusing toward the interstitium]. The present model does not explicitly take into account epithelial and endothelial cell barriers. As seen in Eq. 7, NO synthesis and consumption in these cell layers are accounted for by “source” or “sink” fluxes into the interstitium and into the lumens of the vessels and tubules. Because endothelial and epithelial solute concentrations are not explicitly determined, the fraction of NO consumption attributed to the interstitium is calculated based on interstitial region concentrations, while the fraction attributed to the tubular or vascular lumen is calculated based on tubular lumen or plasma concentrations (13).

Generation and consumption of superoxide.

Studies on kidney homogenates from normotensive and hypertensive rats have suggested that endothelial and epithelial superoxide synthesis is inhibited by low Po₂ (5). Thus the O₂⁻ generation rate is modeled by the following Michaelis-Menten relationship:

$$G_{i,{\text{O}}_2^{-}}=G_{i,{\text{O}}_2^{-}}^{\max }\left[\frac{C_{i,{\text{O}}_2}\left(x\right)}{K_{{\text{O}}_2}^{{\text{O}}_2^{-}}+C_{i,{\text{O}}_2}\left(x\right)}\right].$$ (8)

where $G_{i,{\text{O}}_2^{-}}^{\max }$ is fixed for vessel or tubule i, and the Michaelis constant $K_{{\text{O}}_2}^{{\text{O}}_2^{-}}$ is set to 20.6 μM (5).

As far as we know, measurements of absolute medullary O₂⁻ concentrations have not been reported. A previous modeling study (13) used measurements of H₂O₂ and its steady-state generation and consumption rates to estimate that interstitial superoxide concentrations are on the order of 1 nM. Thus the basal rate of O₂⁻ synthesis in the vasa recta is chosen to give predicted values of interstitial superoxide concentrations ∼1 nM. The ratios between basal O₂⁻ generation rates in the vasa recta and the descending limbs, ascending limbs, and CDs are based on experimental results from microdissected rat nephron segments (31).

Superoxide scavenges NO (rate V₂, Eq. 3) and in turn is consumed by superoxide dismutase (SOD). The reaction rate for this process is

$$V_{i,5}=k_{\text{SOD}}{C}_{i,{\text{O}}_2}^{-}{C}_{i,\text{SOD}},$$ (9)

which takes place in all compartments (13). The total volumetric rate of O₂⁻ consumption in tubule or vessel i is thus given by

$$R_{i,{\text{O}}_2^{-}}=V_{i,2}+V_{i,5}.$$ (10)

As was the case with NO, the fraction of O₂⁻ consumption attributed to the interstitium is calculated based on interstitial region concentrations, while the fraction attributed to the tubular or vascular lumen is calculated based on tubular lumen or plasma concentrations (13).

Sources of NO and O₂⁻ from capillary endothelium.

As little quantitative data are available on the capillary network in the medulla, we assume that the capillaries are well mixed with the local interstitium. To represent production of NO and O₂⁻ by the capillary endothelium, it is assumed that the endothelium releases NO and superoxide directly into the surrounding interstitial region. The maximum NO and O₂⁻ generation rates in the capillaries are taken to be the same as in the vasa recta (13).

O₂ consumption.

In the model, basal O₂ consumption (i.e., for processes other than sodium transport) is assumed to take place in the vascular endothelial cells, tubular epithelial cells, and interstitial cells, and O₂ consumption due to active sodium transport occurs in the medullary proximal straight tubules (PSTs), thick ascending limbs, and CDs. The volumetric rate of basal O₂ consumption in tubule or vas rectum i is given by

$$R_{i,{\text{O}}_2}^{\text{basal}}=R_{\max ,{\text{O}}_2}^{\text{basal}}\left[\frac{C_{i,{\text{O}}_2}\left(x\right)}{K_{\text{M,}i}^{{\text{O}}_2}+C_{i,{\text{O}}_2}\left(x\right)}\right],$$ (11)

where C_i,O2 is the O₂ concentration in tubule or vessel i, K_M,i^O₂ is the Michaelis constant, and R_max,O2^basal is the maximal volumetric rate of O₂ consumption. Here, R_max,O2^basal is taken to be 10 μM/s (4).

To account for the inhibition by NO of mitochondrial utilization, K_M,i^O₂ is varied according to the local NO concentration as follows:

$$K_{\text{M,}i}^{{\text{O}}_2}=K_{\text{M},{\text{O}}_2}\left(1+\frac{C_{i,\text{NO}}}{C_{\text{NO}}^{\text{inhib}}}\right),$$ (12)

where K_M,O2 is the Michaelis constant in the absence of NO and C_NO^inhib is the NO concentration that doubles K_M,i^O₂. Here, they are taken to be 1 mmHg and 27 nM (3), respectively.

In the PSTs, TALs, and CDs, sodium is actively reabsorbed via basolateral Na⁺-K⁺- ATPase pumps; the stoichiometry of metabolic reactions suggests that under maximal efficiency, the number of Na⁺ moles actively reabsorbed per mole of O₂ consumed is 18. That is, the T_Na-to-Q_O2 (where T_Na denotes the moles of Na⁺ transported and Q_O2 denotes the amount of O₂ consumed, also abbreviated as TQ) ratio is 18 for active transport. Under favorable thermodynamic conditions, additional moles of Na⁺ may be reabsorbed paracellularly, which then raises the TQ ratio; on the other hand, unfavorable thermodynamic conditions lower the TQ ratio. In the model, TQ ratios are fixed at 18 for the TAL and PST and 12 for the CD, based on tubular epithelial transport simulations (37, 62). We further assume that below some critical Po₂ (denoted P_i,c for tubule i), anaerobic metabolism maintains some fraction (denoted F_AN) of the energy required to actively transport Na⁺. The rate of active O₂ consumption in the epithelia of the PSTs, TALs, and CDs is then given by

$$R_{i{\text{,O}}_2}^{\text{active}}=\frac{2\pi r_i}{A_i^{\text{epi}}}\frac{{\Psi }_{i,\text{Na}}^{\text{active}}}{{\text{TQ}}_i}\Theta \left(P_{i,{\text{O}}_2}\right),$$ (13)

where r_i is the inner radius of tubule i, TQ_i is the TQ ratio, Ψ_i,Na^active is the Na⁺ active transport rate, and Θ(P_i,O2) is the fraction of that rate that is supported by aerobic respiration, given by

$$\Theta \left(P_{i,{\text{O}}_2}\right)=\{\begin{array}{cc}1,\hfill & {\text{PO}}_2\ge P_{i,c};\hfill \\ \frac{{\text{PO}}_2/P_{i,c}}{F_{\text{AN}}+\left(1-F_{\text{AN}}\right)\left({\text{PO}}_2/P_{i,c}\right)},\hfill & {\text{PO}}_2<P_{i,c}.\hfill \end{array}$$ (14)

The values of parameters P_i,c and F_AN are discussed in the subsequent section.

Active Na⁺ transport.

The volumetric active Na⁺ transport rate is characterized in the model assuming Michaelis-Menten kinetics

$${\Psi }_{i\text{,Na}}^{\text{active}}=V_{\max ,i,\text{Na}}\left[\frac{C_{i,\text{Na}}\left(x\right)}{K_{\text{M,Na}}+C_{i,\text{Na}}\left(x\right)}\right],$$ (15)

where C_i,Na is the Na⁺ concentration in tubule i, V_max,i,Na [in nmol/(cm²·s)] is the maximal rate of Na⁺ transport, and K_M,Na is the Michaelis constant (taken here to be 70 mM; Refs. 17, 29). When luminal Po₂ drops below some critical level, the maximum rate of Na⁺ transport may become limited by O₂ concentration.

In addition, Na⁺ transport is inhibited by NO and stimulated by O₂⁻ (16, 38, 39, 40, 45, 50, 51, 57, 61). The effects of O₂, NO, and O₂⁻ availability on active Ψ_i,Na^active are individually taken into account as follows

$$V_{\max ,i,\text{Na}}=V_{\max ,i,\text{Na}}^{*}\cdot f\left(C_{i,{\text{O}}_2}\right)\cdot g\left(C_{i,\text{NO}}\right)\cdot h\left(C_{i,{\text{O}}_2^{-}}\right),$$ (16)

where $V_{\mathrm{max,i,Na}}^{*}$ is the maximal rate of Na⁺ transport when O₂ is not limiting and in the absence of NO and O₂⁻ (13). As described above, it is assumed that below some critical Po₂ (P_i,c), anaerobic metabolism will supply some of the energy needed to actively transport Na⁺, so that, in the complete absence of O₂, a fraction (F_AN) of the active transport when O₂ is abundant is maintained. This gives

$$f\left(C_{i,{\text{O}}_2}\right)=\{\begin{array}{cc}1,\hfill & {\text{PO}}_2\ge P_{i,c};\hfill \\ {\text{PO}}_2/P_{i,c}\left(1-F_{\text{AN}}\right)+F_{\text{AN}},\hfill & {\text{PO}}_2<P_{i,c}.\hfill \end{array}$$ (17)

We assume that P_i,c = 10 mmHg (15) in all tubules. The value of F_AN is taken to be 0.5 in the outer medullary CD (OMCD) (60, 68), 0.4 in the inner medullary CD (IMCD) (56), 0.1 in the TALs (1), and 0.14 in the PSTs (11).

In vitro experiments have demonstrated that NO inhibits active solute transport across rat TALs (38, 40) and mouse cortical CDs (50), although studies on NO effects specifically on IM Na⁺ transport are lacking. In the present model, the inhibitory effects of NO on active Na⁺ transport are taken into account by assuming that the active transport rate decreases with increasing NO concentration as follows

$$g\left(C_{i,\text{NO}}\right)=1-\frac{C_{i,\text{NO}}}{{\beta }_i+C_{i,\text{NO}}},$$ (18)

where C_i,NO is the NO concentration in tubule or vessel i and β_i is the Michaelis constant. In the TAL, Ortiz et al. (40) found that 10 μM spermine NONOate (SPM, an NO donor) inhibits chloride reabsorption by 46%. With a 10 μM SPM concentration, a bath NO concentration of 50–60 nM is expected (52). Thus β_i is assumed to be 47 nM in the TALs. In the CD, Pech et al. (50) found that 10 μM MAHMA NONOate (another NO donor) reduces chloride flux by ∼50%. Assuming a physiological level of NO, β_i is set to 232 nM in the CDs, so that an average baseline CD NO concentration results in a 50% reduction in active transport. In the PSTs, there is conflicting experimental evidence concerning stimulating/inhibiting effects of NO and O₂⁻ on active Na⁺ transport (38, 45, 51, 61); thus it is assumed in the model that NO and O₂⁻ neither inhibit nor stimulate active Na⁺ transport in the PST.

In vitro studies in the rat have shown that O₂⁻ stimulates Na⁺ transport in the TAL (39) and may do the same in the CD (16, 57), independently of NO. The model takes into account the stimulating effects of O₂⁻ on active Na⁺ transport in the TALs and CDs by assuming that the active transport rate increases with increasing O₂⁻ concentration as follows (13)

$$h\left(C_{i,{\text{O}}_2^{-}}\right)=0.7+0.6\left(\frac{C_{i,{\text{O}}_2^{-}}}{{\gamma }_i+C_{i,{\text{O}}_2^{-}}}\right),$$ (19)

where $C_{i,{\text{O}}_2^{-}}$ is the O₂⁻ concentration in tubule or vessel i and i is a Michaelis constant. The values of i are chosen so that h ∼ 1 in the base case. Based on baseline simulations, i is set to 0.2 pM in the TALs and 0.06 pM in the CDs.

Full model equations and transport parameters not described above, as well as CD inflow boundary conditions, can be found in Refs. 4, 13, 15, 25. Inlet flow rates and solute concentrations for the descending vessels and tubules are listed in Table 1, and maximum NO and O₂⁻ generation rates are listed in Table 2.

Table 1.

Boundary conditions for descending tubules and vessels at x = 0

				DVR
	SDL	LDL	CD	Plasma	RBC
Fv,* nl/min	10	12	6.5	6	2
CNa, mM	160	160	80.5	163.7	163.7
Curea, mM	15	15	152.7	8	8
CO2, μM	15.2	15.2	15.2	60.4	60.4
CNO, nM	100	100	100	100	0.1
$C_{{\text{O}}_2^{-}}$, pM	20	20	20	100	100
CHbNO, μM	0	0	0	0	1
CHbO2, mM	0	0	0	0	17.3
CHb, mM	0	0	0	0	3.0

SDL/LDL, descending limb of short/long loop of Henle; CD, collecting ducts; DVR, descending vasa recta; RBC, red blood cells; C, concentration.

^*Fluid flows (F_v) are given for individual tubules or vessels.

Table 2.

Base case maximum and average generation rates and average consumption rates for NO and O₂⁻ in the tubules and vessels

	NO			O2−
	Max generation	Avg generation	Avg consumption	Max generation	Avg generation	Avg consumption
CD
OM	0.415	3.20 × 10−2	4.10 × 10−5	1.8	5.59 × 10−5	8.34 × 10−4
IM		3.59 × 10−2	8.67 × 10−5		6.05 × 10−5	2.52 × 10−4
LAL
OM	0.985	0.103	5.87 × 10−5	3.2	1.25 × 10−4	1.40 × 10−3
IM		0.143	4.40 × 10−5		1.58 × 10−4	5.31 × 10−4
LDL
OM	12.3	1.27	5.11 × 10−4	15.2	5.91 × 10−4	9.96 × 10−3
IM		1.60	2.05 × 10−4		7.04 × 10−4	2.19 × 10−3
DVR
OM	76.6	19.2	3.81 × 10−4	21.0	1.50 × 10−3	2.20 × 10−2
IM		15.5	1.01 × 10−4		1.30 × 10−3	5.73 × 10−3

Consumption rates are in μM/s. NO, nitric oxide; LAL, ascending limb of long loops of Henle, IM, inner medulla; OM, outer medulla.

RESULTS

Base case results.

Figure 2A shows region Po₂ profiles in the base case. As described in our previous model of oxygen transport in the rat medulla (15), the structure of the OM, in particular, the separation of the O₂-supplying DVR from the active O₂-consuming TALs, generates a substantial radial Po₂ gradient across the regions. This gradient continues throughout the upper IM, where the CD clusters are separated from the DVR. This medullary structure preserves oxygen delivery to the deep IM but leaves the TALs in the OM vulnerable to hypoxic injury.

Fig. 2.

Region Po₂ (mmHg) vs. depth (cm) in the 6 cases. A: base case. B: g_active,NO = 1. C: $h_{\text{active,}{\text{O}}_2^{-}}$ = 0.7. D: g_active,NO = 1 and $h_{\text{active,}{\text{O}}_2^{-}}$ = 0.7. E: DVR inflow 12 nl/min. F: DVR inflow 6 nl/min. Outer medullary (OM)/IM boundary at 0.2 cm.

In Fig. 3A, NO concentrations are given in the four regions. Once again, a noticeable radial gradient exists, with NO levels higher in R3 and R4 than in R1 and R2 throughout the medulla. This occurs because NO consumption rates in the RBCs of the DVR (DRBCs, located in R1 and R2) are orders of magnitude larger than in other structures, as hemoglobin scavenges NO at a rate proportional to the Hb concentration. Between the OM and IM, there is a large increase in NO concentrations in R3 and R4, due to increases in net NO generation in the descending and ascending limbs (resulting from higher Po₂ levels), as the latter move into R4 in the IM (Table 2).

Fig. 3.

Region NO concentration (nM) vs. depth (cm) in the 6 cases. A: base case. B: g_active,NO = 1. C: $h_{\text{active,}{\text{O}}_2^{-}}$ = 0.7. D: g_active,NO = 1 and $h_{\text{active,}{\text{O}}_2^{-}}$ = 0.7. E: DVR inflow 12 nl/min. F: DVR inflow 6 nl/min. OM/IM boundary at 0.2 cm.

Region concentrations of superoxide are given in Fig. 4A. Whereas O₂⁻ concentrations are much lower than NO concentrations, there is still a substantial radial gradient in the interstitial regions. In the OM, superoxide concentrations are highest in R1 and R2, near the vascular bundles, as better oxygenation results in a higher rate of O₂⁻ synthesis. In the IM, O₂⁻ concentrations are consistently lower in R2 and R3 than in R1 and R4, as no O₂-supplying DVR are left in R2 at this depth, and more capillary flow is directed to R4. Moreover, superoxide concentrations in all regions decline fairly steadily throughout the axial length of the medulla, as O₂⁻ consumption rates are larger than rates of O₂⁻ synthesis throughout (Table 2).

Fig. 4.

Region O₂⁻ concentration (nM) vs. depth (cm) in the 6 cases. A: base case. B: g_active,NO = 1. C: $h_{\text{active,}{\text{O}}_2^{-}}$ = 0.7. D: g_active,NO = 1 and $h_{\text{active,}{\text{O}}_2^{-}}$ = 0.7. E: DVR inflow 12 nl/min. F: DVR inflow 6 nl/min. OM/IM boundary at 0.2 cm.

Measurements of medullary NO concentrations generally range from 60 to 100 nM (23, 58, 72), with one study reporting an order-of-magnitude larger value, ∼800 nM (53). The predictions of the model generally lie within this range, with base-case region NO concentrations averaging 45 nM in the OM and 110 nM in the IM. Measurements of medullary O₂⁻ concentrations have not been made directly, to the best of our knowledge. Previous models of NO and O₂⁻ transport suggest that O₂⁻ concentrations are on the order of 0.1 to 1 nM (3, 13). The present model predicts base-case region O₂⁻ concentrations averaging 1.5 nM in the OM and 0.28 nM in the IM, which is consistent with previous modeling studies.

Effects of stimulation/inhibition of sodium transport by NO and O₂⁻.

In the next set of simulations, we aimed to assess the impact NO and superoxide have on sodium transport in the medulla, beginning with NO. To that end, we conducted a simulation in which NO-mediated inhibition of active Na⁺ transport was abolished. That is, g(C_i,NO) was set to 1 in equation (16). [In the base case, g(C_i,NO) < 1.] Without NO affecting sodium transport, total TAL Na⁺ reabsorption increases by 38%. As a result, urine NaCl flow rate drops by 32% (from 0.198 to 0.134 nmol·min⁻¹·nephron⁻¹). The higher Na⁺ reabsorption rate raises interstitial fluid osmolality and water reabsorption from tubules and vessels. Thus urine flow decreases by 17% and urine osmolality increases from 1,215 to 1,223 mosmol/kgH₂O (Table 3). In addition, Po₂ decreases throughout the regions (Fig. 2B), as O₂-consuming active NaCl transport increases in the OM and IM. There is a slight reduction in region superoxide concentrations (Fig. 4B) and a significant reduction in region NO concentrations (Fig. 3B), due to the decreasing rate of NO and O₂⁻ production with decreasing Po₂. Overall, these results suggest that NO elicits a significant reduction in Na⁺ reabsorption and urine osmolality under basal conditions.

Table 3.

Urine water flow rates, solute concentrations, and osmolalities for the different cases

Case	Water Flow	[Na], mM	[Urea], mM	Po2, mmHg	[NO], nM	[O2−], fM	Osmolality, mosmol/kgH2O
(1) Base	0.706	281	598	3.31	83.9	3.82	1215
(2) g(CNO) = 1	0.586	228	679	2.75	78.7	3.30	1223
(3) h($C_{{\text{O}}_2^{-}}$) = 0.7	0.769	312	539	4.13	94.6	4.54	1205
(4) g(CNO) = 1, h($C_{{\text{O}}_2^{-}}$) = 0.7	0.688	246	627	3.03	80.4	3.57	1184
(5) $G_{{\text{O}}_2^{-}}^{\max }$ × 10	0.693	263	609	2.66	72.6	31.3	1197
(6) $G_{{\text{O}}_2^{-}}^{\max }$ × 10, TQ × ½	0.737	309	551	1.46	47.8	18.7	1215
(7) $G_{{\text{O}}_2^{-}}^{\max }$ × 0.5	0.694	262	611	2.24	48.4	27.5	1195
(8) $G_{{\text{O}}_2^{-}}^{\max }$ × 0.5, TQ × ½	0.736	308	552	1.28	34.4	16.8	1214
(9) DVR inflow = 12 nl/min	0.909	210	520	6.81	122	6.44	987
(10) DVR inflow = 9 nl/min	0.740	262	578	4.21	96.5	4.59	1157
(11) DVR inflow = 7 nl/min	0.650	312	625	2.47	68.6	3.03	1307
(12) DVR inflow = 6 nl/min	0.630	329	635	1.31	31.7	1.84	1354
(13) SNGFR = 42 nl/min	3.59	137	381	5.60	71.3	5.82	662
(14) SNGFR = 24 nl/min	0.223	377	643	2.72	91.5	3.23	1572

Urine water flow rates are in nmol·min⁻¹·nephron⁻¹. Square brackets indicate concentration. SNGFR, single nephron glomerular filtration rate.

Next, we examined the extent to which superoxide affects active sodium transport by conducting a simulation in which O₂⁻-mediated stimulation of active Na⁺ transport was abolished. That is, h($C_{i,{\text{O}}_2^{-}}$) was set to 0.7 in Eq. 16. [In the base case, h($C_{i,{\text{O}}_2^{-}}$) > 0.7.] In the absence of such stimulative effects, total TAL Na⁺ reabsorption decreases by 47%, and urine NaCl flow rate increases by 21% (from 0.198 to 0.240 nmol·min⁻¹·nephron⁻¹). The concentrating capacity of the model is slightly reduced, with an increase in urine flow from 0.706 to 0.769 nl/min and a decrease in urine osmolality from 1,215 to 1,205 mosmol/kgH₂O (Table 3). In addition, Po₂ increases throughout the regions (Fig. 2C), and the resulting higher rates of NO and O₂⁻ production are evident in the noticeably higher region NO and O₂⁻ concentrations (Figs. 3C and 4C). In other words, the model predicts that under basal conditions O₂⁻ substantially raises Na⁺ reabsorption to the detriment of medullary O₂ levels.

To study these competing effects of NO and O₂⁻ on oxygenation and urine NaCl flow, we conducted a simulation in which both the NO and O₂⁻ effects on the maximum active transport rate were removed. That is, g(C_i,NO) was set to 1, and h(C_i,O2⁻) was set to 0.7 in Eq. 16. The net result is a 29% increase in TAL Na⁺ reabsorption and a 15% decrease in urine NaCl flow (from 0.198 to 0.169 nmol·min⁻¹·nephron⁻¹). Po₂ decreases significantly throughout the regions (Fig. 2D), following more closely the NO-decoupled case than the O₂⁻-decoupled case. The lower Po₂ decreases NO production rate, resulting in significantly lower interstitial NO concentrations (similar to the NO-decoupled case, with minor differences). Region O₂⁻ concentrations also decrease slightly due to the lower O₂⁻ production rate with lower Po₂.

It is somewhat surprising that removing the effects of both NO and O₂⁻ on Na⁺ transport yield a less concentrated urine than removing only the effect of O₂⁻, given the diuretic effect of NO (see Table 3). This result can be attributed to the nonlinear interactions among O₂, NO, and O₂⁻, as concentrations of these solutes, used to determine V_max,i,Na in Eq. 16, change significantly with g(C_i,NO) or h($C_{i,{\text{O}}_2^{-}}$) set to constant values. In the inner stripe, where most of the active Na⁺ transport takes place, V_max,i,Na is lowest in the case where the effects of both NO and O₂⁻ are removed. This is due to the nonlinear effects of O₂, NO, and O₂⁻, for even though Po₂ is higher in this case than in the NO-decoupled case, the additional removal of O₂⁻ stimulation of active Na⁺ transport is enough to sufficiently lower V_max,i,Na (see Fig. 6). This in turn causes osmolality to be lowest in this case.

Fig. 6.

Feedback loop outlining the effects of O₂, NO, and O₂⁻ on active NaCl transport rate. Solid lines indicate effects on production rate, dashed lines indicate effects on consumption rate, and dotted lines indicate effects on active NaCl transport rate (T_Na). Arrows at the ends of lines indicate stimulation (or increase), whereas circles at the ends of lines indicate inhibition (or decrease).

Effects of sodium load on Po₂ and NO and O₂⁻ concentrations.

Given the interdependence among the transport of Na⁺, O₂, NO, and O₂⁻, we then investigated the influence of Na⁺ delivery on Po₂ and NO and O₂⁻ concentrations. To examine this, we varied the single nephron glomerular filtration rate (SNGFR) from 80 to 140% of its base-case value, that is, from 24 to 42 nl/min in the superficial nephrons and from 28.8 to 50.4 nl/min in the juxtamedullary nephrons (where base-case values are 30 and 36 nl/min, respectively).

Figure 5, A and B, shows values of effective ascending limb and CD V_max vs. depth as SNGFR is varied, and Fig. 5C shows R4 Po₂. In the OM, when SNGFR increases, V_max increases overall and R4 Po₂ decreases. Conversely, in the IM, when SNGFR increases, V_max decreases and R4 Po₂ increases. This difference in behavior comes from the dependence of V_max on NO and O₂⁻. Per se, the higher SNGFR enhances Na⁺ reabsorption and thus reduces Po₂. This lowers NO and O₂⁻ production, which in turn affects V_max. The net effect on V_max is nonmonotonic, since NO inhibits and O₂⁻ stimulates Na⁺ reabsorption (i.e., lower NO and O₂⁻ concentrations does not necessarily imply higher or lower V_max; it could be either, depending on the exact values of NO and O₂⁻ concentrations). As a consequence of this nonlinear behavior (Fig. 6), the predicted effects of an increase in SNGFR on V_max (and thus Po₂) are different in the OM and IM.

Fig. 5.

Effective ascending limb V_max (A), effective CD V_max (B), and R4 Po₂ (C) vs. depth for superficial single nephron glomerular filtration rates (SNGFRs) of 24, 30 (base case), 36, and 42 nl/min.

Furthermore, urine Po₂ is predicted to increase by 69% over base case when superficial nephron SNGFR is increased to 42 nl/min; conversely, there is an 18% decrease in urine Po₂ when SNGFR decreases to 24 nl/min (Table 3). Table 3 also shows that when SNGFR increases, urine flow increases, and urine osmolality decreases; in addition, overall Na⁺ excretion increases with increasing SNGFR (as can be calculated from Table 3).

Effects of hypertension.

In hypertension, angiotensin II induces oxidative stress (32, 43), resulting in significantly lower renal tissue Po₂ (42, 44, 64, 65). Reduced NO formation diminishes renal tissue Po₂ further by decreasing medullary blood flow and therefore O₂ supply. To simulate oxygenation in a hypertensive kidney, we raised the superoxide generation rate, $G_{i,{\text{O}}_2^{-}}^{\max }$ by a factor of 10. As expected, the higher rate of superoxide production results in larger O₂⁻ concentrations in the regions and a significantly higher urine O₂⁻ concentration (Table 3). However, the increase in O₂⁻ concentration is severely damped by corresponding increases in superoxide consumption rates when O₂⁻ generation rates are increased. In addition, region Po₂ and NO concentrations decrease, as higher superoxide levels stimulate NaCl reabsorption. As a result, urine NaCl flow rate decreases by 8.1% from 0.198 to 0.182 nmol·min⁻¹·nephron⁻¹.

Some evidence from in vivo rat micropuncture experiments exists suggesting that NO and/or reactive oxygen species limit the number of moles of Na⁺ that can be actively reabsorbed per mole of O₂ consumed (63). Data from spontaneously hypertensive rats (64) suggest that the TQ ratio may be approximately halved when superoxide concentrations are significantly increased. Thus we simulated the situation where the superoxide generation rate was kept at 10 times the base-case value, while the TQ ratio for active sodium transport was halved. Lowering the TQ ratio significantly lowered Po₂ and urine O₂ flow rate (Table 3), as expected. In addition, urine NO flow rate (Table 3) and region NO concentrations were significantly decreased, due again to the fact that lower Po₂ results in a lower NO generation rate. Furthermore, urine NaCl flow rate increased to 0.228 nmol·min⁻¹·nephron⁻¹ (calculated from Table 3), as NaCl active transport efficiency was reduced by half.

Some hypertensive rat models have indicated a decrease in NO production as well (33). Thus, we simulated a 50% decrease in the NO generation rate, along with a 10-fold increase in the O₂⁻ generation rate. Decreasing the NO generation rate by 50% decreased Po₂ and NO and O₂⁻ region concentrations. In addition, with a 50% decrease in NO production, the urine osmolality fell to 1,195 mosmol/kgH₂O. However, there was little effect on the urine NaCl flow rate, which remained at 0.182 nmol·min⁻¹·nephron⁻¹ (calculated from Table 3).

In addition, when the TQ ratio was halved, urine flow rates and osmolalities increased (Table 3); however, Po₂ and NO and O₂⁻ concentrations were significantly decreased. The impact of the $G_{i,{\text{O}}_2^{-}}^{\max }$ increase, G_i,NO^max decrease, and TQ ratio decrease on average R4 inner stripe Po₂ is shown in Fig. 7. This interstitial region (R4), which contains the short ascending limb and CD (Fig. 1), was chosen as a proxy for a vulnerable part of the kidney to hypoxia, as it had a consistently lower Po₂ than other regions and depths (see, for example, Fig. 2A). As can be seen in Fig. 7, all simulated hypertensive conditions resulted in lower Po₂ levels than the base-case value of 7.9 mmHg. Increasing the O₂⁻ generation rate decreased the Po₂ by 8.3%, with little change when G_i,NO^max was lowered by 50% in addition. However, lowering the TQ ratio by 50% further decreased Po₂ by another 44%, suggesting that elevated oxidative stress (represented by a 10-fold increase in $G_{i,{\text{O}}_2^{-}}^{\max }$) has much less of an impact on tissue oxygenation than metabolic dysfunction (represented by a halving of the TQ ratio) in hypertension.

Fig. 7.

Average R4 inner stripe Po₂ in the base case and under hypertensive conditions.

Effects of vascular inflow.

Blood flow in the medulla increases when renal hydrostatic pressure in the interstitium is elevated and is known to be modulated by the antidiuretic hormone (6, 7, 41, 59). To determine what effect medullary blood flow has on NO and superoxide, vascular inflow was varied between 6 and 12 nl/min at the cortico-medullary boundary (base-case inflow was 8 nl/min).

We first increased DVR inflow to 12 nl/min. Urine water flow increased by 29% (from 0.706 to 0.909 nl·min⁻¹·nephron⁻¹), and urine Po₂ increased 2.1-fold (from 3.31 to 6.81 mmHg). Due to washout from high DVR flow rate, urine osmolality decreased by 19%, from 1,215 to 987 mosmol/kgH₂O. Region Po₂ increased significantly in both the OM and IM (Fig. 2E), with significant increases in region NO and O₂⁻ concentrations (Figs. 3E and 4E).

When the DVR flow rate was progressively lowered, Po₂ and NO and O₂⁻ concentrations decreased concomitantly, accompanied by a steady increase in urine osmolality (Table 3). At the lower end, DVR inflow was decreased by 25% relative to base case, to 6 nl/min. Urine water flow decreased by 11% (from 0.706 to 0.630 nl·min⁻¹·nephron⁻¹), and urine Po₂ decreased by 60% (from 3.31 to 1.31 mmHg). Due to less washout from DVR flow, urine osmolality increased by 11%, from 1,215 to 1,354 mosmol/kgH₂O. Region Po₂ decreased significantly in both the OM and IM (Fig. 2F), with significant decreases in region NO and O₂⁻ concentrations (Figs. 3F and 4F).

DISCUSSION

We extended a highly detailed mathematical model of NO and superoxide transport in the rat renal OM (13) to include the IM. The model yields predictions of NaCl, urea, O₂, NO, and O₂⁻ concentrations in all represented structures (and of Hb, HbO₂, and HbNO in the RBCs), as well as water and solute flow rates in all tubules and vessels. The model uses a region-based approach to represent the radial organization of medullary tubules and vessels, centered around vascular bundles in the OM and CD clusters in the IM. Model predictions suggest that the balance between NO and O₂⁻ affects medullary oxygenation and urine osmolality and that the nonlinear interactions between these solutes and oxygen lead to effects that cannot be determined by examining each in isolation. Furthermore, the results of the model shed some light on the mechanisms underlying the pathway to medullary hypoxia in hypertension and suggest that urine Po₂ could serve as a biomarker for medullary hypoxia.

Comparison with experimental results.

NO concentration measurements in the rat renal IM range from 60 to 120 nM, generally measured in the upper half of the IM. In one study, NO concentration was measured as 79 nM at a depth of 1.5 mm below the OM-IM boundary (58). In another study at the same depth, NO concentration was measured as ∼120 nM (23). In a third study using the rat kidney, an NO concentration of ∼105 nM was measured at 1 mm below the OM-IM boundary (72). Model predictions from the present study generally lie within this range throughout the IM, with small discrepancies: NO concentration averages 24 nM in R1, 16 nM in R2, 100 nM in R3, and 293 nM in R4. Due to the highly structured organization of the renal medulla, the model predicts large radial and axial gradients in NO concentration; thus average predicted NO concentrations are on the same order of magnitude as experimental measurements but with a fairly large variation.

In the OM, one study measured NO concentration as ∼796 nM, using differential pulsed voltammetry (53), a different technique than the one used in the other studies. Model predictions in the OM are noticeably below this value, closer to the experimental range measured in the IM: NO concentration averages 23 nM in R1, 21 nM in R2, 74 nM in R3, and 61 nM in R4. Because these predictions are similar to measurements in other parts of the medulla, it is likely that the discrepancy is due to the difference in experimental technique, one that yields a measurement an order of magnitude larger than previous experiments.

As also noted in Base case results, we are unaware of direct measurements of O₂⁻ concentration in the renal medulla. Previous modeling work suggests that O₂⁻ concentrations lie in the range of 0.1 to 1 nM (3, 13), and model predictions from the present study are generally contained within this interval throughout the OM and IM. In the OM, predicted O₂⁻ concentrations average 2.2 nM in R1, 1.9 nM in R2, 1.0 nM in R3, and 0.97 nM in R4. In the IM, predicted O₂⁻ concentrations average 0.50 nM in R1, 0.14 nM in R2, 0.16 nM in R3, and 0.32 nM in R4. If experimental measurements of O₂⁻ concentration in the renal medulla are made in the future, we will be able to better validate these model predictions.

Comparison with previous models.

The main difference between the present model and our previous NO and O₂⁻ transport model (13) is that the current one includes the whole medulla, whereas the old one included only the OM. The most important consequence of this change is that the current model allows for explicit prediction of IM flow rates, concentrations, and papillary outflows, instead of making bulk assumptions about IM behavior based on the OM model. For instance, the previous NO-O₂⁻ model assumed that O₂ consumption in the IM was a fixed 5% of O₂ supply to the OM; however, simulations from the present model that explicitly include the IM architecture predict that IM O₂ consumption is 11% of medullary O₂ supply. Thus our current whole medulla model provides a richer set of predictions than the previous study.

In contrast with our previous whole medulla O₂ transport model (15), the present model explicitly represents NO and O₂⁻ and thus takes into account the nonlinear interactions among O₂, NO, and O₂⁻. Specifically, the previous model did not take into account the impact of NO and O₂⁻ on Po₂ via modulation of the active transport of NaCl and the concomitant modulation of O₂ consumption. In particular, the previous O₂ model predicted interstitial Po₂ levels ∼2–3 mmHg lower than the current model; this discrepancy is largely due to NO inhibition of active sodium transport in the current model, which leads to higher Po₂ levels. This reveals the mitigating effects of NO on medullary hypoxia that could not be gleaned from our previous study.

Feedback among O₂, NO, and O₂⁻.

Results of the model suggest that NO and O₂⁻ significantly modulate renal function. However, the effects of NO and superoxide on NaCl transport cannot be considered in isolation, due to the feedback loops among O₂, NO, and O₂⁻ (Fig. 6).

The generation rates of both NO and O₂⁻ are oxygen dependent, with higher Po₂ resulting in a higher production rate. In a previous model (13), we considered two possibilities for Po₂ effects on O₂⁻ synthesis, both inhibition and stimulation. Results from Chen et al. (5) provided stronger evidence for the latter case, demonstrating a drop in O₂⁻ production during hypoxia; thus, we assumed stimulating effects in the present study.

The consumption rates of O₂, NO, and O₂⁻ are all interdependent, as well. Both NO and superoxide are consumed at rates proportional to the product of the local NO and O₂⁻ concentrations; thus the two solutes are mutual scavengers. In addition, due to the dependence of the Michaelis constant in Eq. 12 on NO, the rate of basal O₂ consumption decreases with increasing NO concentration.

All of these solutes then affect the rate of active NaCl transport, which itself modulates Po₂. As seen in Eq. 16, the maximum NaCl transport rate increases with increases in oxygen and superoxide concentration and decreases with growing NO concentrations.

NO and O₂⁻ scavenge each other and have opposite effects on NaCl transport and therefore on O₂ consumption. Given these complicated interactions among oxygen, NO, and superoxide, a somewhat unexpected result is that NO and O₂⁻ concentrations seem to always vary in tandem with Po₂. This strong Po₂ dependence of medullary NO and O₂⁻ concentrations suggests that medullary oxygenation may be a primary factor in the regulation of blood flow and blood pressure in the kidney.

Urine salt excretion.

An important aspect of medullary function that the present whole medulla model can predict, whereas previous models could not, is the impact of NO and superoxide on urine salt excretion. In the base case, which includes the effects of NO and O₂⁻ on NaCl active transport, urine sodium flow rate is predicted to be 0.198 nmol·min⁻¹·nephron⁻¹.

If NO did not have an inhibitory effect on active NaCl transport, urine sodium flow rate would drop by 32% (to 0.134 nmol·min⁻¹·nephron⁻¹); however, due to a concomitant decrease in urine water flow rate, urine osmolality would slightly increase. In other words, the net impact of NO is to lower urine osmolality. Conversely, if O₂⁻ did not have a stimulating effect on active NaCl transport, urine sodium flow rate would rise by 21% (to 0.240 nmol·min⁻¹·nephron⁻¹), but urine osmolality would slightly decrease due to an increase in urine water flow rate. Stated differently, the net impact of O₂⁻ is to raise urine osmolality. If neither NO nor O₂⁻ had an effect on NaCl active transport, urine water and sodium flow rates would both decrease compared with the base case, such as in the absence of NO effects only, but urine osmolality would also noticeably decrease. Due to the nonlinear feedback loops, the effect on osmolality of removing both NO- and O₂⁻-mediated regulation is not merely an average of the effects of removing NO- and O₂⁻-mediated regulation in isolation. That is, it is the combined effect of NO and O₂⁻ that helps to keep urine osmolality at a higher level. We should point out that the model does not assume that NO and O₂⁻ are from the same enzyme source. To the best of our knowledge, the principal enzymes that catalyze the production of NO and superoxide, NO synthases and NADPH oxidases, are different under most conditions. Under diabetic conditions, endothelial dysfunction can result in endothelial NO synthase (eNOS) “uncoupling,” which may lead to eNOS producing superoxide instead of (or in addition to) NO (18). The concentrations we are matching to infer the NO and O₂⁻ generation rates do not involve diabetes; thus we are implicitly assuming that the enzymes that catalyze their formation sources are different in this model.

Hypertension.

Renal tissue Po₂ has been shown to be significantly lower in several models of experimental hypertension, including the spontaneously hypertensive rat; the two-kidney, one-clip model; and angiotensin II-induced hypertension (42, 44, 64, 65). One contributing factor for low renal tissue Po₂ in hypertension is the increased oxidative stress induced by angiotensin II. Elevated oxidative stress reduces tubular transport efficiency, causes mitochondrial uncoupling, and leads to increased O₂ consumption (43). Furthermore, reduced NO formation increases tubular transport but reduces O₂ supply.

Model results suggest that a sufficiently large reduction in tubular transport efficiency may be the key contributing factor to hypertension-induced medullary hypoxia (Table 2). More specifically, under hypertensive conditions, and no change in the TQ ratio, urine sodium excretion and osmolality both decrease (by 8.1 and 1.6%, respectively). If it is assumed that hypertension further results in a 50% decrease in the TQ ratio, osmolality increases back to base-case levels, and urine sodium excretion increases above base-case levels. However (see Fig. 7), a reduction in the TQ ratio results in a significant decrease in Po₂, potentially leaving the kidney vulnerable to hypoxic injury. This indicates that elevated oxidative stress on its own may have less impact than the subsequent metabolic dysfunction on the progression of medullary hypoxia due to hypertension.

Other factors, not considered in the present study, also contribute to the development of renal hypoxia in a hypertensive kidney. At the onset of hypertension, renal autoregulation effectively prevents the transmission of the elevated systolic blood pressure to the glomeruli or peritubular capillaries. Renal autoregulation is mediated by several mechanisms: the myogenic response, which is a property of the preglomerular vasculature wherein a rise in intravascular pressure elicits a reflex constriction that generates a compensatory increase in vascular resistance; and tubuloglomerular feedback, a negative feedback response that balances glomerular filtration rate with tubular reabsorptive capacity (10, 19, 22). However, as hypertension progresses, renal arteries, including the afferent arterioles, undergo pathological alterations, such that vasodilation becomes impaired. Autoregulation is compromised, and as a consequence a temporary reduction in blood pressure can impair renal perfusion (20, 24). In the absence of a compensatory increase in O₂ delivery, these pathological changes may also explain renal tissue hypoxia and thus eventually, chronic kidney diseases.

Urine Po₂ as a biomarker.

The present model allowed us to investigate whether urinary Po₂ could be used as a biomarker for renal hypoxia, which is a pathway to acute kidney injury (AKI). As a motivation, we note that AKI is a prevalent complication of surgical procedures including cardiac surgeries that require cardiopulmonary bypass (24). Diagnosis of AKI is usually based on either an elevation of serum creatinine or the detection of oliguria (34). Serum creatinine is a poor marker of early renal dysfunction, because its serum concentration is greatly influenced by numerous nonrenal factors (e.g., body weight, race, age, gender, total body volume, drugs, muscle metabolism, and protein intake) (2). The utility of serum creatinine is worse in AKI, because the patients are not in steady state; hence, serum creatinine lags far behind renal injury. Thus substantial rises in serum creatinine are often not witnessed until 48–72 h after the initial insult to the kidney (34, 55).

Evans et al. (14) recently suggested that urine in the CDs should equilibrate with tissue Po₂ in the IM. Accordingly, the Po₂ of urine in the renal pelvis may change in response to stimuli that would be expected to alter oxygenation of the renal medulla. Thus they proposed that urinary Po₂ may be a predictor of AKI risk in hospital settings. It is noteworthy that the renal structures that are most susceptible to hypoxic injuries are the TALs and proximal tubules in the OM; therefore, even if urinary Po₂ equilibrates with the IM tissue Po₂, what does it tell us about the OM, a much more vulnerable region?

We thus analyzed our simulation results to determine the relationship between OM tissue and urinary Po₂. Note that these simulations do not represent the most common conditions that lead to hospital-acquired AKI, e.g., cardiac surgery performed under cardiopulmonary bypass. Rather, model parameters were adjusted to simulate hypertension and other conditions that affect medullary oxygenation. Nonetheless, we hoped to obtain new insights regarding the potential of urinary Po₂ as a prognostic tool to guide the on-going management of renal health in patients. We compared urinary Po₂ against the luminal Po₂ of the most vulnerable segment, i.e., the short TAL in the inner stripe, for all the cases considered in Table 3. Model results, shown in Fig. 8, indicate a strong correlation between urinary and short TAL Po₂. The lone outlier is case 3 (with h_active,SOX = 0.7), where the effect of O₂⁻ on TAL active transport is disabled, producing a substantially higher medullary Po₂. This case bears little resemblance to the physiological conditions that lead to AKI. Thus our model simulations suggest that urinary Po₂ may be used as a prognostic tool in monitoring the renal health in patients undergoing surgeries with AKI as a known complication, especially in patients with hypertension, diabetes, and chronic kidney diseases, who are believed to be at elevated risk for developing hospital-acquired AKI.

Fig. 8.

Urine Po₂ vs. average inner stripe short ascending limb (IS SAL) Po₂ (mmHg) for all cases in results. Numbers (1–14) correspond to those listed in Table 3 (e.g., marker “9” in figure corresponds to the urine Po₂ and average inner stripe short ascending limb Po₂ in the “DVR inflow = 12 nl/min” simulation).

Model limitations and future extensions.

The model in the present study is necessarily limited by the dearth of experimental data concerning medullary NO and superoxide. As noted above, measurements of NO in the medulla vary over an order of magnitude, and we are unaware of any absolute measurements of O₂⁻ in the medulla. Thus experiments measuring NO and superoxide levels at various depths of the renal medulla would help to validate model assumptions concerning baseline generation rates. In addition, model parameters related to the effects of NO and O₂⁻ on active Na⁺ transport are uncertain, due a lack of quantitative data. We estimated these processes and values based on the scarce available data, but measurements of transport rates or reabsorption in the presence of different amounts of NO and O₂⁻ would allow for better estimation of parameters in the model. That being said, it is precisely because experimental studies in this area are difficult and scarce that a modeling approach can be helpful. Predictions from the model provide suggestions for future experiments. In particular, the predicted relationships among NO, O₂⁻, and Po₂ suggest experiments involving alteration of renal Po₂ and determining what effect (if any) this has on regulation of blood pressure and renal blood flow; the results of such experiments could either be used to validate our modeling approach or serve as a guide to improve the model.

Renal oxygenation is the result of a delicate balance between O₂ supply and demand, and that relation changes in diseased states. The present model represents solute transport and reactions in the renal medulla; however, the renal autoregulatory mechanisms, which control renal and medullary blood flow and thus O₂ supply, are not represented. Medullary blood flow is assumed to be known a priori, even though NO is known to cause vasodilation and to increase blood flow. Hence, the present model cannot be used to assess the extent to which impairment of renal autoregulation in diseases such as diabetes and hypertension (see above) gives rise to renal hypoxia. It is our goal to extend the present model to represent the whole kidney (similar to Ref. 36) and to incorporate tubuloglomerular feedback and the myogenic response. The autoregulatory mechanisms can be represented using our published model (54). The resulting model could then be used to study the development of renal hypoxia in diabetes and hypertension and the mechanisms underlying the pathways to chronic kidney diseases.

GRANTS

This research was supported by National Institute of Diabetes and Digestive and Kidney Diseases Grant DK-089066.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

Author contributions: B.C.F., A.E., and A.T.L. conception and design of research; B.C.F. performed experiments; B.C.F., A.E., and A.T.L. analyzed data; B.C.F., A.E., and A.T.L. interpreted results of experiments; B.C.F. prepared figures; B.C.F. and A.T.L. drafted manuscript; B.C.F., A.E., and A.T.L. edited and revised manuscript; B.C.F., A.E., and A.T.L. approved final version of manuscript.