Time-varying properties of renal autoregulatory mechanisms

Renal autoregulation in health and disease

Intrarenal autoregulatory mechanisms maintain renal blood flow (RBF) and glomerular filtration rate (GFR) independent of renal perfusion pressure (RPP) over a defined range (80-180 mmHg). Such autoregulation is mediated largely by the myogenic and the macula densa-tubuloglomerular feedback (MD-TGF) responses that regulate preglomerular vasomotor tone primarily of the afferent arteriole. Differences in response times allow separation of these mechanisms in the time and frequency domains. Mechanotransduction initiating the myogenic response requires a sensing mechanism activated by stretch of vascular smooth muscle cells (VSMCs) and coupled to intracellular signaling pathways eliciting plasma membrane depolarization and a rise in cytosolic free calcium concentration ([Ca(2+)]i). Proposed mechanosensors include epithelial sodium channels (ENaC), integrins, and/or transient receptor potential (TRP) channels. Increased [Ca(2+)]i occurs predominantly by Ca(2+) influx through L-type voltage-operated Ca(2+) channels (VOCC). Increased [Ca(2+)]i activates inositol trisphosphate receptors (IP3R) and ryanodine receptors (RyR) to mobilize Ca(2+) from sarcoplasmic reticular stores. Myogenic vasoconstriction is sustained by increased Ca(2+) sensitivity, mediated by protein kinase C and Rho/Rho-kinase that favors a positive balance between myosin light-chain kinase and phosphatase. Increased RPP activates MD-TGF by transducing a signal of epithelial MD salt reabsorption to adjust afferent arteriolar vasoconstriction. A combination of vascular and tubular mechanisms, novel to the kidney, provides for high autoregulatory efficiency that maintains RBF and GFR, stabilizes sodium excretion, and buffers transmission of RPP to sensitive glomerular capillaries, thereby protecting against hypertensive barotrauma. A unique aspect of the myogenic response in the renal vasculature is modulation of its strength and speed by the MD-TGF and by a connecting tubule glomerular feedback (CT-GF) mechanism. Reactive oxygen species and nitric oxide are modulators of myogenic and MD-TGF mechanisms. Attenuated renal autoregulation contributes to renal damage in many, but not all, models of renal, diabetic, and hypertensive diseases. This review provides a summary of our current knowledge regarding underlying mechanisms enabling renal autoregulation in health and disease and methods used for its study.

Laser speckle contrast imaging reveals large-scale synchronization of cortical autoregulation dynamics influenced by nitric oxide

Synchronization of tubuloglomerular feedback (TGF) dynamics in nephrons that share a cortical radial artery is well known. It is less clear whether synchronization extends beyond a single cortical radial artery or whether it extends to the myogenic response (MR). We used LSCI to examine cortical perfusion dynamics in isoflurane-anesthetized, male Long-Evans rats. Inhibition of nitric oxide synthases by N(ω)-nitro-l-arginine methyl ester (l-NAME) was used to alter perfusion dynamics. Phase coherence (PC) was determined between all possible pixel pairs in either the MR or TGF band (0.09-0.3 and 0.015-0.06 Hz, respectively). The field of view (≈4 × 5 mm) was segmented into synchronized clusters based on mutual PC. During the control period, the field of view was often contained within one cluster for both MR and TGF. PC was moderate for TGF and modest for MR, although significant in both. In both MR and TGF, PC exhibited little spatial variation. After l-NAME, the number of clusters increased in both MR and TGF. MR clusters became more strongly synchronized while TGF clusters showed small highly coupled, high-PC regions that were coupled with low PC to the remainder of the cluster. Graph theory analysis probed modularity of synchronization. It confirmed weak synchronization of MR during control that probably was not physiologically relevant. It confirmed extensive and long-distance synchronization of TGF during control and showed increased modularity, albeit with larger modules seen in MR than in TGF after l-NAME. The results show widespread synchronization of MR and TGF that is differentially affected by nitric oxide.

Signal transduction in a compliant thick ascending limb

In several previous studies, we used a mathematical model of the thick ascending limb (TAL) to investigate nonlinearities in the tubuloglomerular feedback (TGF) loop. That model, which represents the TAL as a rigid tube, predicts that TGF signal transduction by the TAL is a generator of nonlinearities: if a sinusoidal oscillation is added to constant intratubular fluid flow, the time interval required for an element of tubular fluid to traverse the TAL, as a function of time, is oscillatory and periodic but not sinusoidal. As a consequence, NaCl concentration in tubular fluid alongside the macula densa will be nonsinusoidal and thus contain harmonics of the original sinusoidal frequency. We hypothesized that the complexity found in power spectra based on in vivo time series of key TGF variables arises in part from those harmonics and that nonlinearities in TGF-mediated oscillations may result in increased NaCl delivery to the distal nephron. To investigate the possibility that a more realistic model of the TAL would damp the harmonics, we have conducted new studies in a model TAL that has compliant walls and thus a tubular radius that depends on transmural pressure. These studies predict that compliant TAL walls do not damp, but instead intensify, the harmonics. In addition, our results predict that mean TAL flow strongly influences the shape of the NaCl concentration waveform at the macula densa. This is a consequence of the inverse relationship between flow speed and transit time, which produces asymmetry between up- and downslopes of the oscillation, and the nonlinearity of TAL NaCl absorption at low flow rates, which broadens the trough of the oscillation relative to the peak. The dependence of waveform shape on mean TAL flow may be the source of the variable degree of distortion, relative to a sine wave, seen in experimental recordings of TGF-mediated oscillations.

Nephron blood flow dynamics measured by laser speckle contrast imaging

Tubuloglomerular feedback (TGF) has an important role in autoregulation of renal blood flow and glomerular filtration rate (GFR). Because of the characteristics of signal transmission in the feedback loop, the TGF undergoes self-sustained oscillations in single-nephron blood flow, GFR, and tubular pressure and flow. Nephrons interact by exchanging electrical signals conducted electrotonically through cells of the vascular wall, leading to synchronization of the TGF-mediated oscillations. Experimental studies of these interactions have been limited to observations on two or at most three nephrons simultaneously. The interacting nephron fields are likely to be more extensive. We have turned to laser speckle contrast imaging to measure the blood flow dynamics of 50-100 nephrons simultaneously on the renal surface of anesthetized rats. We report the application of this method and describe analytic techniques for extracting the desired data and for examining them for evidence of nephron synchronization. Synchronized TGF oscillations were detected in pairs or triplets of nephrons. The amplitude and the frequency of the oscillations changed with time, as did the patterns of synchronization. Synchronization may take place among nephrons not immediately adjacent on the surface of the kidney.

Continuous estimates of dynamic cerebral autoregulation during transient hypocapnia and hypercapnia

Dynamic cerebral autoregulation (CA) is the transient response of cerebral blood flow (CBF) to rapid blood pressure changes: it improves in hypocapnia and becomes impaired during hypercapnia. Batch-processing techniques have mostly been used to measure CA, providing a single estimate for an entire recording. A new approach to increase the temporal resolution of dynamic CA parameters was applied to transient hypercapnia and hypocapnia to describe the time-varying properties of dynamic CA during these conditions. Thirty healthy subjects (mean +/- SD: 25 +/- 6 yr, 9 men) were recruited. CBF velocity was recorded in both middle cerebral arteries (MCAs) with transcranial Doppler ultrasound. Arterial blood pressure (Finapres), end-tidal CO(2) (ET(CO(2)); infrared capnograph), and a three-lead ECG were also measured at rest and during repeated breath hold and hyperventilation. A moving window autoregressive moving average model provided continuous values of the dynamic CA index [autoregulation index (ARI)] and unconstrained gain. Breath hold led to significant increase in ET(CO(2)) (+5.4 +/- 6.1 mmHg), with concomitant increase in CBF velocity in both MCAs. Continuous dynamic CA parameters showed highly significant changes (P < 0.001), with a temporal pattern reflecting a delayed dynamic response of CA to changes in arterial Pco(2) and a maximal reduction in ARI of -5.1 +/- 2.4 and -5.1 +/- 2.3 for the right and left MCA, respectively. Hyperventilation led to a marked decrease in ET(CO(2)) (-7.2 +/- 4.1 mmHg, P < 0.001). Unexpectedly, CA efficiency dropped significantly with the inception of the metronome-controlled hyperventilation, but, after approximately 30 s, the ARI increased gradually to show a maximum change of 5.7 +/- 2.9 and 5.3 +/- 3.0 for the right and left MCA, respectively (P < 0.001). These results confirm the potential of continuous estimates of dynamic CA to improve our understanding of human cerebrovascular physiology and represent a promising new approach to improve the sensitivity of clinical applications of dynamic CA modeling.

Unexpected effect of angiotensin AT1 receptor blockade on tubuloglomerular feedback in early subtotal nephrectomy

After subtotal nephrectomy (STN), the remaining nephrons engage in hyperfiltration, which may be facilitated by a reduced sensitivity of the tubuloglomerular feedback (TGF) response to increased distal delivery. However, a muted TGF response would contradict the notion of remnant kidney as a prototype of angiotensin II (ANG II) excess, since ANG II normally sensitizes the TGF response and stimulates proximal reabsorption. We examined the role of ANG II as a modulator of TGF and proximal reabsorption in 7 days after STN in male rats. Single-nephron glomerular filtration rate (SNGFR) and proximal reabsorption (J(prox)) were measured in late proximal collections while perfusing Henle's loop for minimal and maximal TGF stimulation in rats treated with the angiotensin type 1 (AT(1)) receptor blocker losartan or placebo in drinking water for 7 days. Perfusion of Henle's loop yielded a robust TGF response in sham-operated rats. In STN, the feedback responses were highly variable and nil, on average. Paradoxical TGF responses to augmented late proximal flow were confirmed in SNGFR measurements from the early distal nephron. Chronic losartan treatment normalized the average TGF response without reducing the variability. J(prox) was subtly affected by chronic losartan in sham surgery or STN, after controlling for differences in SNGFR. However, when administered acutely into the early S1 segment, losartan potently suppressed J(prox) in STN and sham-operated rats alike. Chronic losartan stabilizes the TGF system in remnant kidneys. This cannot be explained by currently known actions of AT(1) receptors but is commensurate with a salutary effect of an intact TGF system on dynamic autoregulation of intraglomerular flow and pressure.

Intracranial pressure waves: characterization of a pulsation absorber with notch filter properties using systems analysis: laboratory investigation

OBJECT

The relationship between the waveform of intracranial pressure (ICP) and arterial blood pressure can be quantitatively characterized using a newly developed technique in systems analysis, the time-varying transfer function. This technique considers the arterial blood pressure as an input signal composed of multiple frequencies represented in the output ICP according to the transfer function imposed by the intracranial system on the input signal. The transfer function can change with time and with physiological manipulations. The authors examined data obtained from canine experiments involving manipulations of ICP.

METHODS

The authors analyzed 11 experiments from 3 normal mongrel dogs under conditions of normal ICP and with changes in ICP made by bolus injection, infusion, or withdrawal of cerebrospinal fluid by using time-varying transfer function.

RESULTS

During normal ICP periods, the gain of the transfer function displayed a deep notch (> or = 1 log unit) centered at or near the cardiac frequency. In systems terms, the intracranial compartment under normal conditions appears to act as a notch filter attenuating the cardiac frequency input relative to other frequencies. Epochs of ICP elevation showed suppression of the notch, and the notch was restored when ICP returned to normal.

CONCLUSIONS

The intracranial system in these animals could be considered to include a pulsation absorber for which the target frequency appears to be close to the cardiac frequency. One possible source for such an absorber mechanism might be the free movement of cerebrospinal fluid, implying that impairment of this motion may have important clinical implications in various neurological conditions such as hydrocephalus.

Analysis of nonstationarity in renal autoregulation mechanisms using time-varying transfer and coherence functions

The extent to which renal blood flow dynamics vary in time and whether such variation contributes substantively to dynamic complexity have emerged as important questions. Data from Sprague-Dawley rats (SDR) and spontaneously hypertensive rats (SHR) were analyzed by time-varying transfer functions (TVTF) and time-varying coherence functions (TVCF). Both TVTF and TVCF allow quantification of nonstationarity in the frequency ranges associated with the autoregulatory mechanisms. TVTF analysis shows that autoregulatory gain in SDR and SHR varies in time and that SHR exhibit significantly more nonstationarity than SDR. TVTF gain in the frequency range associated with the myogenic mechanism was significantly higher in SDR than in SHR, but no statistical difference was found with tubuloglomerular (TGF) gain. Furthermore, TVCF analysis revealed that the coherence in both strains is significantly nonstationary and that low-frequency coherence was negatively correlated with autoregulatory gain. TVCF in the frequency range from 0.1 to 0.3 Hz was significantly higher in SDR (7 out of 7, >0.5) than in SHR (5 out of 6, <0.5), and consistent for all time points. For TGF frequency range (0.03-0.05 Hz), coherence exhibited substantial nonstationarity in both strains. Five of six SHR had mean coherence (<0.5), while four of seven SDR exhibited coherence (<0.5). Together, these results demonstrate substantial nonstationarity in autoregulatory dynamics in both SHR and SDR. Furthermore, they indicate that the nonstationarity accounts for most of the dynamic complexity in SDR, but that it accounts for only a part of the dynamic complexity in SHR.

Representation of time-varying nonlinear systems with time-varying principal dynamic modes

System identification of nonlinear time-varying (TV) systems has been a daunting task, as the number of parameters required for accurate identification is often larger than the number of data points available, and scales with the number of data points. Further, a 3-D graphical representation of TV second-order nonlinear dynamics without resorting to taking slices along one of the four axes has been a significant challenge to date. In this paper, we present a TV principal dynamic mode (TVPDM) method which overcomes these deficiencies. The TVPDM, by design, reduces one dimension, and by projecting PDM coefficients onto a set of basis functions, both nonstationary and nonlinear dynamics can be characterized. Another significant advantage of the TVPDM is its ability to discriminate the signal from noise dynamics, and provided that signal dynamics are orthogonal to each other, it has the capability to separate them. The efficacy of the proposed method is demonstrated with computer simulation examples comprised of various forms of nonstationarity and nonlinearity. The application of the TVPDM to the human heart rate and arterial blood pressure data during different postures is also presented and the results reveal significant nonstationarity even for short-term data recordings. The newly developed method has the potential to be a very useful tool for characterizing nonlinear TV systems, which has been a significant, challenging problem to date.

Calcium signaling in vasopressin-induced aquaporin-2 trafficking

It has been the general consensus that cAMP-mediated PKA-dependent phosphorylation of aquaporin-2 is the primary mechanism of vasopressin to regulate osmotic water permeability in kidney collecting duct. By using laser scanning confocal microscopy to monitor [Ca2+]i and apical exocytosis in individual cells of inner medullary collecting duct, we have demonstrated that vasopressin also triggers intracellular Ca2+ mobilization, which is coupled to apical exocytotic insertion of aquaporin-2. Vasopressin-induced Ca2+ mobilization is in the form of oscillations, which involves both intracellular Ca2+ release from ryanodine-gated Ca2+ stores and extracellular Ca2+ influx via capacitative calcium entry. Each individual cell operates as an independent calcium oscillator with time variance in frequency and amplitude. Vasopressin-induced Ca2+ mobilization is mediated by cAMP, but is independent of PKA. Exogenous cAMP analog (8-pCPT-2'-O-Me-cAMP), which activates Epac (exchange protein directly activated by cAMP), but not PKA, triggers Ca2+ mobilization and apical exocytosis. These observations suggest that activation of Epac by cAMP may also contribute to the action of vasopressin in regulating osmotic water permeability. There are multiple plausible candidates for downstream effectors of vasopressin-induced Ca2+ signal including calmodulin, myosin light chain kinase, calmodulin kinase II, and calcineurin. All of them have been implicated in the regulation of aquaporin-2 trafficking and/or water permeability.

Frequency modulation of renal myogenic autoregulation by perfusion pressure

Recent studies of renal autoregulation have shown modulation of the faster myogenic mechanism by the slower tubuloglomerular feedback and that the modulation can be detected in the dynamics of the myogenic mechanism. Conceptual and empirical considerations suggest that perfusion pressure may modulate the myogenic mechanism, although this has not been tested to date. Here we present data showing that the myogenic operating frequency, assessed by transfer-function analysis, varied directly as a function of perfusion pressure in the hydronephrotic kidney perfused in vitro over the range from 80 to 140 mmHg. A similar result was obtained in intact kidneys in vivo when renal perfusion pressure was altered by systemic injection of NG-nitro-l-arginine methyl ester (l-NAME). When perfusion pressure was not allowed to increase, l-NAME did not affect the myogenic operating frequency despite equivalent reduction of renal vascular conductance. Blood-flow dynamics were assessed in the superior mesenteric artery before and after l-NAME. In this vascular bed, the operating frequency of the myogenic mechanism was not affected by perfusion pressure. Thus the operating frequency of the renal myogenic mechanism is modulated by perfusion pressure independently of tubuloglomerular feedback, and the data suggest some degree of renal specificity of this response.

Interactions contributing to kidney blood flow autoregulation

PURPOSE OF REVIEW

Autoregulation of renal blood flow has traditionally been considered to stabilize glomerular filtration, and thus tubular load, in the face of blood pressure fluctuations. This view arose because of the contribution of tubuloglomerular feedback, which senses distal tubular fluid composition, to regulation and autoregulation of renal blood flow. Studies have indicated a more important role for the myogenic mechanism. It has been proposed that the 'purpose' of autoregulation is to defend glomerular structure. Both these views may be incomplete because neither takes into consideration the complex interactions between tubuloglomerular feedback and the myogenic mechanism and among nephrons whose afferent arterioles derived from a common interlobular artery.

RECENT FINDINGS

Recent findings indicate that it is now indisputable that effective autoregulation is necessary for defense of glomerular structure. Extensive modulation of the myogenic mechanism by tubuloglomerular feedback has been shown using a variety of experimental designs that have illuminated one pathway (neuronal nitric oxide synthase at the macula densa) by which this occurs.

SUMMARY

These findings indicate that the myogenic mechanism can no longer be considered as a purely vascular mechanism in the kidney and instead receives information via tubuloglomerular feedback about the status of renal function.

Assessment of renal autoregulation

The kidney displays highly efficient autoregulation so that under steady-state conditions renal blood flow (RBF) is independent of blood pressure over a wide range of pressure. Autoregulation occurs in the preglomerular microcirculation and is mediated by two, perhaps three, mechanisms. The faster myogenic mechanism and the slower tubuloglomerular feedback contribute both directly and interactively to autoregulation of RBF and of glomerular capillary pressure. Multiple experiments have been used to study autoregulation and can be considered as variants of two basic designs. The first measures RBF after multiple stepwise changes in renal perfusion pressure to assess how a biological condition or experimental maneuver affects the overall pressure-flow relationship. The second uses time-series analysis to better understand the operation of multiple controllers operating in parallel on the same vascular smooth muscle. There are conceptual and experimental limitations to all current experimental designs so that no one design adequately describes autoregulation. In particular, it is clear that the efficiency of autoregulation varies with time and that most current techniques do not adequately address this issue. Also, the time-varying and nonadditive interaction between the myogenic mechanism and tubuloglomerular feedback underscores the difficulty of dissecting their contributions to autoregulation. We consider the modulation of autoregulation by nitric oxide and use it to illustrate the necessity for multiple experimental designs, often applied iteratively.

Mechanisms of renal blood flow autoregulation: dynamics and contributions

Autoregulation of renal blood flow (RBF) is caused by the myogenic response (MR), tubuloglomerular feedback (TGF), and a third regulatory mechanism that is independent of TGF but slower than MR. The underlying cause of the third regulatory mechanism remains unclear; possibilities include ATP, ANG II, or a slow component of MR. Other mechanisms, which, however, exert their action through modulation of MR and TGF are pressure-dependent change of proximal tubular reabsorption, resetting of RBF and TGF, as well as modulating influences of ANG II and nitric oxide (NO). MR requires < 10 s for completion in the kidney and normally follows first-order kinetics without rate-sensitive components. TGF takes 30-60 s and shows spontaneous oscillations at 0.025-0.033 Hz. The third regulatory component requires 30-60 s; changes in proximal tubular reabsorption develop over 5 min and more slowly for up to 30 min, while RBF and TGF resetting stretch out over 20-60 min. Due to these kinetic differences, the relative contribution of the autoregulatory mechanisms determines the amount and spectrum of pressure fluctuations reaching glomerular and postglomerular capillaries and thereby potentially impinge on filtration, reabsorption, medullary perfusion, and hypertensive renal damage. Under resting conditions, MR contributes approximately 50% to overall RBF autoregulation, TGF 35-50%, and the third mechanism < 15%. NO attenuates the strength, speed, and contribution of MR, whereas ANG II does not modify the balance of the autoregulatory mechanisms.

Interactions between TGF-dependent and myogenic oscillations in tubular pressure and whole kidney blood flow in both SDR and SHR

We previously showed that nonlinear interactions between the two renal autoregulatory mechanics (tubuloglomerular feedback and the myogenic mechanism) were observed in the stop flow pressure (SFP) and whole kidney blood flow data from Sprague-Dawley rats (SDR) using time-invariant bispectrum analysis ( 3 , 4 ). No such nonlinear interactions were observed in either SFP or whole kidney blood flow data obtained from spontaneously hypertensive rats (SHR). We speculated that the failure to detect nonlinear interactions in the SHR data may be related to our observation that these interactions were not continuous and therefore had time-varying characteristics. Thus the absence of such nonlinear interactions may be due to an inappropriate time-invariant method being applied to data that are especially time varying in nature. We examine this possibility in this paper by using a time-varying bispectrum approach, which we developed for this purpose. Indeed, we found significant nonlinear interactions in SHR ( n = 18 for SFP; n = 12 for whole kidney blood flow). Moreover, the duration of nonlinear coupling is found statistically to be longer ( P = 0.001) in SFP data from either SDR or SHR than it is in whole kidney data from either type of rat. We conclude that nonlinear coupling is present at both the single nephron as well as the whole kidney level for SDR and SHR. In addition, SHR data at the whole kidney level exhibit the most transient nonlinear coupling phenomena.

A Robust Method for Detection of Linear and Nonlinear Interactions: Application to Renal Blood Flow Dynamics

We have developed a method that can identify switching dynamics in time series, termed the improved annealed competition of experts (IACE) algorithm. In this paper, we extend the approach and use it for detection of linear and nonlinear interactions, by employing histograms showing the frequency of switching modes obtained from the IACE, then examining time-frequency spectra. This extended approach is termed Histogram of improved annealed competition of experts-time frequency (HIACE-TF). The hypothesis is that frequent switching dynamics in HIACE-TF results are due to interactions between different dynamic components. To validate this assertion, we used both simulation examples as well as application to renal blood flow data. We compared simulation results to a time-phase bispectrum (TPB) approach, which can also be used to detect time-varying quadratic phase coupling between various components. We found that the HIACE-TF approach is more accurate than the TPB in detecting interactions, and remains accurate for signal-to-noise ratios as low as 15 dB. With all 10 data sets, comprised of volumetric renal blood flow data, we also validated the feasibility of the HIACE-TF approach in detecting nonlinear interactions between the two mechanisms responsible for renal autoregulation. Further validation of the HIACE-TF approach was achieved by comparing it to a realistic mathematical model that has the capability to generate either the presence or the absence of nonlinear interactions between two renal autoregulatory mechanisms.

Very low frequency modulation in renal autoregulation

This study aims to examine the presence of a possible third renal autoregulatory mechanism in the very low frequency (VLF) band (approximately 10 mHz) using a high-resolution time- frequency spectral method. Blood pressure and renal blood flow data were measured from conscious and anesthetized Sprague-Dawley and spontaneously hypertensive rats, at the level of the whole kidney (via ultrasound flow probe) and local cortical tissue of a kidney (via laser Doppler flow probe). In addition, N-nitro-L-arginine (LNAME) was used in order to assess the effect of nitric oxide on the third mechanism. Using a complex demodulation method with high time and frequency resolution, a VLF band was often observed, as well as amplitude modulation at the VLF of the two other autoregulation mechanisms. The presence of amplitude modulation is an indication of a particular form of nonlinear interaction between the autoregulatory mechanisms. Physically, such interactions may arise from the fact that all three mechanisms share a common effector, the afferent arteriole. In addition, the magnitude of amplitude modulation of the VLF on the other autoregulatory mechanisms was enhanced by the addition of LNAME, suggesting an important role of nitric oxide in the autoregulatory process.

Multistability in tubuloglomerular feedback and spectral complexity in spontaneously hypertensive rats

Single-nephron proximal tubule pressure in spontaneously hypertensive rats (SHR) can exhibit highly irregular oscillations similar to deterministic chaos. We used a mathematical model of tubuloglomerular feedback (TGF) to investigate potential sources of the irregular oscillations and the corresponding complex power spectra in SHR. A bifurcation analysis of the TGF model equations, for nonzero thick ascending limb (TAL) NaCl permeability, was performed by finding roots of the characteristic equation, and numerical simulations of model solutions were conducted to assist in the interpretation of the analysis. These techniques revealed four parameter regions, consistent with TGF gain and delays in SHR, where multiple stable model solutions are possible: 1) a region having one stable, time-independent steady-state solution; 2) a region having one stable oscillatory solution only, of frequency f1; 3) a region having one stable oscillatory solution only, of frequency f2, which is approximately equal to 2f1; and 4) a region having two possible stable oscillatory solutions, of frequencies f1 and f2. In addition, we conducted simulations in which TAL volume was assumed to vary as a function of time and simulations in which two or three nephrons were assumed to have coupled TGF systems. Four potential sources of spectral complexity in SHR were identified: 1) bifurcations that permit switching between different stable oscillatory modes, leading to multiple spectral peaks and their respective harmonic peaks; 2) sustained lability in delay parameters, leading to broadening of peaks and of their harmonics; 3) episodic, but abrupt, lability in delay parameters, leading to multiple peaks and their harmonics; and 4) coupling of small numbers of nephrons, leading to multiple peaks and their harmonics. We conclude that the TGF system in SHR may exhibit multistability and that the complex power spectra of the irregular TGF fluctuations in this strain may be explained by switching between multiple dynamic modes, temporal variation in TGF parameters, and nephron coupling.

Qualification of arterial stiffness as a risk factor to the progression of chronic kidney diseases

BACKGROUND

Reflection pressure may influence the clinical course of chronic kidney diseases (CKDs). The relationship between the augmentation index (AI) and progression of non-diabetic CKDs was characterized.

METHODS

Ninety-nine patients were enrolled into the study. Pulse wave form analysis was performed to determine AI that assesses arterial stiffness.

RESULTS

In a cross-sectional study, a multiple regression analysis found that AI correlated positively to age and weight, and negatively to height and heart rate (R(2) = 0.50). Furthermore, echocardiography was performed in 51 patients who gave their consent. In male patients under angiotensin inhibition, left ventricular mass index increased as AI was elevated (r = 0.33, slope = 0.85 +/- 0.30 g/m(2)/%, p < 0.05, n = 23). A prospective study was performed in 41 patients who consented to having their creatinine clearance measured repeatedly. In the patients with angiotensin inhibition a higher basal AI resulted in a greater annual decrease in creatinine clearance (r = -0.52, slope = -0.43 +/- 0.14 ml/min/year/%, p < 0.01, n = 27).

CONCLUSION

The present data indicate that AI as well as angiotensin contribute to the development of left ventricular hypertrophy. Furthermore, our results suggest that in addition to angiotensin, AI is a risk factor of progression of non-diabetic CKDs.

Identification of Transient Renal Autoregulatory Mechanisms Using Time-Frequency Spectral Techniques

Identification of the two principal mediators of renal autoregulation from time-series data is difficult, as both the tubuloglomerular feedback (TGF) and myogenic (MYO) mechanisms interact and share a common effector, the afferent arteriole. Moreover, although both mechanisms can exhibit oscillations in well-characterized frequency bands, these systems often operate in nonoscillatory states not detectable by frequency-domain analysis. To overcome these difficulties, we have developed a new approach to the characterization of the TGF and MYO systems. A laser Doppler probe is used to measure fluctuations in local cortical blood flow (CBF) in response to spontaneous changes in blood pressure (BP) and to large imposed perturbations in BP, which elicit strong, simultaneous, transient, oscillatory blood flow responses. These transient responses are identified by high-resolution time-frequency spectral analysis of the time-series data. In this report, we compare four different time-frequency spectral techniques (the short-time Fourier transform (STFT), smoothed pseudo Wigner-Ville, and two recently developed methods: the Hilbert-Huang transform and time varying optimal parameter search (TVOPS)) to determine which of these four methods is best suited for the identification of transient oscillations in renal autoregulatory mechanisms. We found that TVOPS consistently provided the best performance in both simulation examples and identification of the two autoregulatory mechanisms in actual data. While the STFT suffers in time and frequency resolution as compared to the other three methods, it was able to identify the two autoregulatory mechanisms. Taken together, our experience suggests a two level approach to the analysis of renal blood flow (RBF) data: STFT to obtain a low-resolution time-frequency spectrogram, followed by the use of a higher resolution technique, such as the TVOPS, if even higher time-frequency resolution of the transient responses is required.

Multiple Time-Varying Dynamic Analysis Using Multiple Sets of Basis Functions

We extend a recently developed algorithm that expands the time-varying parameters onto a single set of basis functions, to multiple sets of basis functions. This feature allows the capability to capture many different dynamics that may be inherent in the system. A single set of basis functions that has its own unique characteristics can best capture dynamics of the system that have similar features. Therefore, for systems that have multiple dynamics, the use of a single set of basis functions may not be adequate. Computer simulation examples do indeed show the benefit of using multiple sets of basis functions over the single set of basis functions for cases with many switching dynamics. Moreover, the proposed method remains accurate even under significant noise contamination. Application of the proposed approach to blood pressure data likewise indicate better tracking capability of the two sets of basis function than the recursive least squares or a single set of basis functions.

Differential effects of salt on renal hemodynamics and potential pressure transmission in stroke-prone and stroke-resistant spontaneously hypertensive rats

Salt-supplemented stroke-prone spontaneously hypertensive rats (SHRsp) develop more severe hypertension-induced renal damage (HIRD) compared with their progenitor SHR. The present studies were performed to examine whether in addition to increasing the severity of hypertension salt also enhanced the transmission of such hypertension to the renal vascular bed in the SHRsp. "Step" and "dynamic" renal blood flow (RBF) autoregulation (AR) were examined in approximately 12-wk-old SHR and SHRsp after 3-5 days of an 8% NaCl diet. During step AR under anesthesia (n = 8-11), RBF was significantly higher in the SHRsp at all perfusion pressures (P < 0.01), but AR capacity was not different. Similarly, in separate conscious chronically instrumented rats (n = 8 each), both blood pressure (BP) and RBF were modestly but significantly higher at baseline before salt in the SHRsp (P < 0.05). However, transfer function analysis did not show significant differences in the admittance gain parameters. However, after 3-5 days of salt, although average BP was not significantly altered in either strain, RBF increased further in the SHRsp and there was a significantly greater transfer of BP into RBF power in the SHRsp. This was reflected in the significantly higher admittance gain parameters at most frequencies including the heartbeat frequency (P < 0.05 maximum). These differential hemodynamic effects of salt have the potential to enhance BP transmission to the renal vascular bed and also contribute to the more severe HIRD observed in the salt-supplemented SHRsp.

Interactions of TGF-dependent and myogenic oscillations in tubular pressure

We have previously shown that there are two oscillating components in spontaneously fluctuating single-nephron blood flow obtained from Sprague-Dawley rats (Yip K-P, Holstein-Rathlou NH, and Marsh DJ. Am J Physiol Renal Physiol 264: F427–F434, 1993). The slow oscillation (20–30 mHz) is mediated by tubuloglomerular feedback (TGF), whereas the fast oscillation (100 mHz) is probably related to spontaneous myogenic activity. The fast oscillation is rarely detected in spontaneous tubular pressure because of its small magnitude and the fact that tubular compliance filters pressure waves. We detected myogenic oscillation superimposed on TGF-mediated oscillation when ambient tubular flow was interrupted. Two well-defined peaks are present in the mean power spectrum of stop-flow pressure (SFP) centering at 25 and 100 mHz ( n = 13), in addition to a small peak at 125–130 mHz. Bispectral analysis indicates that two of these oscillations (30 and 100 mHz) interact nonlinearly to produce the third oscillation at 125–130 mHz. The presence of nonlinear interactions between TGF and myogenic oscillations indicates that estimates of the relative contribution of each of these mechanisms in renal autoregulation need to account for this interaction. The magnitude of myogenic oscillations was considerably smaller in the SFP measured from spontaneously hypertensive rats (SHR, n = 13); consequently, nonlinear interactions were not observed with bispectral analysis. Reduced augmentation of myogenic oscillations in SFP of SHR might account for the failure in detecting nonlinear interactions in SHR.

Robust Algorithm for Estimation of Time-Varying Transfer Functions

We introduce a new method to estimate reliable time-varying (TV) transfer functions (TFs) and TV impulse response functions. The method is based on TV autoregressive moving average models in which the TV parameters are accurately obtained using the optimal parameter search method which we have previously developed. The new method is more accurate than the recursive least-squares (RLS), and remains robust even in the case of significant noise contamination. Furthermore, the new method is able to track dynamics that change abruptly, which is certainly a deficiency of the RLS. Application of the new method to renal blood pressure and flow revealed that hypertensive rats undergo more complex and TV autoregulation in maintaining stable blood flow than do normotensive rats. This observation has not been previously revealed using time-invariant TF analyses. The newly developed approach may promote the broader use of TV system identification in studies of physiological systems and makes linear and nonlinear TV modeling possible in certain cases previously thought intractable.

Governance of arteriolar oscillation by ryanodine receptors

To investigate the role of ryanodine receptors in glomerular arterioles, experiments were performed using an isolated perfused hydronephrotic kidney model. In the first series of studies, BAYK-8644 (300 nM), a calcium agonist, constricted afferent (19.6 +/- 0.6 to 17.6 +/- 0.5 microm, n = 6, P < 0.01) but not efferent arterioles. Furthermore, BAYK-8644 elicited afferent arteriolar oscillatory movements. Subsequent administration of nifedipine (1 microM) inhibited both afferent arteriolar oscillation and constriction by BAYK-8644 (to 19.4 +/- 0.5 microm). In the second group, although BAYK-8644 constricted afferent arterioles treated with 1 microM of thapsigargin (19.7 +/- 0.6 to 16.8 +/- 0.6 microm, n = 5, P < 0.05), it failed to induce rhythmic contraction. Removal of extracellular calcium with EGTA (2 mM) reversed BAYK-8644-induced afferent arteriolar constriction (to 20.0 +/- 0.5 microm). In the third series of investigations, ryanodine (10 microM) but not 2-aminoethoxyphenyl borate (100 microM) abolished afferent arteriolar vasomotion by BAYK-8644. In the fourth series of experiments, in the presence of caffeine (1 mM), the stronger activation of voltage-dependent calcium channels by higher potassium media resulted in greater afferent arteriolar constriction and faster oscillation. Our results indicate that L-type calcium channels are rich in preglomerular but not postglomerular microvessels. Furthermore, the present findings suggest that either prolonged calcium influx through voltage-dependent calcium channels (BAYK-8644) or sensitized ryanodine receptors (caffeine) is required to trigger periodic calcium release through ryanodine receptors in afferent arterioles.