Interactions of TGF-dependent and myogenic oscillations in tubular pressure

Glomerular microcirculation: Implications for diabetes, preeclampsia, and kidney injury

This review outlines the features of tandem regulation of glomerular microcirculation by autoregulatory mechanisms and intraglomerular redistribution of blood flow. Multiple points of cooperation exist between autoregulatory and distributional mechanisms. Mutual interactions between myogenic and tubuloglomerular feedback (TGF) mechanisms regulating the inflow are briefly discussed. In addition to this, TGF operation involving purinergic, autocoid, and NO signaling affects, however, not only afferent arteriolar tone, but mesangial cell tone as well. The latter reversibly reconfigures the distribution of blood flow between the shorter and longer pathways in the glomerular tuft. I advance a hypothesis that blood flow in these pathways spontaneously alternates, and mesangial cell tonicity serves as a rheostatic shift between them. Furthermore, humoral messengers from macula densa cells, themselves dependent on myogenic mechanisms, fine-tune the secretion of renin and, subsequently, the local, intrarenal generation of angiotensin II, which, in turn, provides additional vasomotor signaling to glomerular capillaries through changing the tone of mesangial cells. This complex regulatory network may partially explain the phenomenon of renal functional reserve, as well as suggest implications for changes in renal function during pregnancy, early diabetes mellitus, and acute kidney injury.

Reduced tubuloglomerular feedback activity and absence of its synchronization in a connexin40 knockout rat

Introduction: Tubuloglomerular feedback (TGF) is the negative feedback component of renal blood flow (RBF) autoregulation. Neighbouring nephrons often exhibit spontaneous TGF oscillation and synchronization mediated by endothelial communication, largely via connexin40 (Cx40). Methods: We had a knockout (KO) rat made that lacks Cx40. One base pair was altered to create a stop codon in exon 1 of Gja5, the gene that encodes Cx40 (the strain is WKY-Gja55em1Mcwi). Blood pressure (BP)-RBF transfer functions probed RBF dynamics and laser speckle imaging interrogated the dynamics of multiple efferent arterioles that reach the surface (star vessels). Results: The distribution of wild type (WT), heterozygote, and KO pups at weaning approximated the Mendelian ratio of 1:2:1; growth did not differ among the three strains. The KO rats were hypertensive. BP-RBF transfer functions showed low gain of the myogenic mechanism and a smaller TGF resonance peak in KO than in WT rats. Laser speckle imaging showed that myogenic mechanism had higher frequency in KO than in WT rats, but similar maximum spectral power. In contrast, the TGF frequency was similar while peak power of its oscillation was much smaller in KO than in WT rats. In WT rats, plots of instantaneous TGF phase revealed BP-independent TGF synchronization among star vessels. The synchronization could be both prolonged and widespread. In KO rats TGF synchronization was not seen, although BP transients could elicit short-lived TGF entrainment. Discussion: Despite the reduced TGF spectral power in KO rats, there was sufficient TGF gain to induce oscillations and therefore enough gain to be effective locally. We conclude that failure to synchronize is dependent, at least in part, on impaired conducted vasomotor responses.

Synchronization in renal microcirculation unveiled with high-resolution blood flow imaging

Internephron interaction is fundamental for kidney function. Earlier studies have shown that nephrons signal to each other, synchronise over short distances, and potentially form large synchronised clusters. Such clusters would play an important role in renal autoregulation, but due to the technological limitations, their presence is yet to be confirmed. In the present study, we introduce an approach for high-resolution laser speckle imaging of renal blood flow and apply it to estimate frequency and phase differences in rat kidney microcirculation under different conditions. The analysis unveiled spatial and temporal evolution of synchronised blood flow clusters of various sizes, including the formation of large (>90 vessels) long-lived clusters (>10 periods) locked at the frequency of the tubular glomerular feedback mechanism. Administration of vasoactive agents caused significant changes in the synchronisation patterns and, thus, in nephrons' co-operative dynamics. Specifically, infusion of vasoconstrictor angiotensin II promoted stronger synchronisation, while acetylcholine caused complete desynchronisation. The results confirm the presence of the local synchronisation in the renal microcirculatory blood flow and that it changes depending on the condition of the vascular network and the blood pressure, which will have further implications for the role of such synchronisation in pathologies development.

Tubuloglomerular Feedback Synchronization in Nephrovascular Networks

To perform their functions, the kidneys maintain stable blood perfusion in the face of fluctuations in systemic BP. This is done through autoregulation of blood flow by the generic myogenic response and the kidney-specific tubuloglomerular feedback (TGF) mechanism. The central theme of this paper is that, to achieve autoregulation, nephrons do not work as single units to manage their individual blood flows, but rather communicate electrically over long distances to other nephrons via the vascular tree. Accordingly, we define the nephrovascular unit (NVU) to be a structure consisting of the nephron, glomerulus, afferent arteriole, and efferent arteriole. We discuss features that require and enable distributed autoregulation mediated by TGF across the kidney. These features include the highly variable topology of the renal vasculature which creates variability in circulation and the potential for mismatch between tubular oxygen demand and delivery; the self-sustained oscillations in each NVU arising from the autoregulatory mechanisms; and the presence of extensive gap junctions formed by connexins and their properties that enable long-distance transmission of TGF signals. The existence of TGF synchronization across the renal microvascular network enables an understanding of how NVUs optimize oxygenation-perfusion matching while preventing transmission of high systemic pressure to the glomeruli, which could lead to progressive glomerular and vascular injury.

The nephron-arterial network and its interactions

Tubuloglomerular feedback and the myogenic mechanism form an ensemble in renal afferent arterioles that regulate single-nephron blood flow and glomerular filtration. Each mechanism generates a self-sustained oscillation, the mechanisms interact, and the oscillations synchronize. The synchronization generates a bimodal electrical signal in the arteriolar wall that propagates retrograde to a vascular node, where it meets similar electrical signals from other nephrons. Each signal carries information about the time-dependent behavior of the regulatory ensemble. The converging signals support synchronization of the nephrons participating in the information exchange, and the synchronization can lead to formation of nephron clusters. We review the experimental evidence and the theoretical implications of these interactions and consider additional interactions that can limit the size of nephron clusters. The architecture of the arterial tree figures prominently in these interactions.

Architecture of the rat nephron-arterial network: analysis with micro-computed tomography

Among solid organs, the kidney's vascular network stands out, because each nephron has two distinct capillary structures in series and because tubuloglomerular feedback, one of the mechanisms responsible for blood flow autoregulation, is specific to renal tubules. Tubuloglomerular feedback and the myogenic mechanism, acting jointly, autoregulate single-nephron blood flow. Each generates a self-sustained periodic oscillation and an oscillating electrical signal that propagates upstream along arterioles. Similar electrical signals from other nephrons interact, allowing nephron synchronization. Experimental measurements show synchronization over fields of a few nephrons; simulations based on a simplified network structure that could obscure complex interactions predict more widespread synchronization. To permit more realistic simulations, we made a cast of blood vessels in a rat kidney, performed micro-computed tomography at 2.5-μm resolution, and recorded three-dimensional coordinates of arteries, afferent arterioles, and glomeruli. Nonterminal branches of arcuate arteries form treelike structures requiring two to six bifurcations to reach terminal branches at the tree tops. Terminal arterial structures were either paired branches at the tops of the arterial trees, from which 52.6% of all afferent arterioles originated, or unpaired arteries not at the tree tops, yielding the other 22.9%; the other 24.5% originated directly from nonterminal arteries. Afferent arterioles near the corticomedullary boundary were longer than those farther away, suggesting that juxtamedullary nephrons have longer afferent arterioles. The distance separating origins of pairs of afferent arterioles varied randomly. The results suggest an irregular-network tree structure with vascular nodes, where arteriolar activity and local blood pressure interact.

Detecting Interactions between the Renal Autoregulation Mechanisms in Time and Space

OBJECTIVE

Our objective is to identify localized interactions between the renal autoregulation mechanisms over time.

METHODS

A time-varying phase-randomized wavelet bicoherence detector for quadratic phase coupling between tubuloglomerular feedback and the myogenic response is presented. Through simulations we show its ability to interrogate quadratic phase coupling. The method is applied to kidney blood flow and laser speckle imaging sequences of cortical perfusion from anesthetized rats before and after nonselective inhibition of nitric-oxide synthase.

RESULTS

Quadratic phase coupling in kidney blood flow data was present in four out of nine animals during the control period for 13.0 ± 5.6% (mean ± SD) of time and in five out of nine animals during inhibition of nitric-oxide synthase for 15.8 ± 8.2% of time. Approximately 60% of time-series extracted from laser speckle imaging pixels of the renal cortex showed significant quadratic phase coupling. Pixels with significant coupling had a median coupling length of 10.8 ± 2.2% and 12.1 ± 3.1% of time with the 95th percentile of pixels being coupled for 25.5 ± 4.4% and 30.9 ± 6.4% of time during control and inhibition of nitric-oxide synthase, respectively.

CONCLUSION

These results indicate quadratic phase coupling exists in short time intervals between tubuloglomerular feedback and the myogenic response and is detected more often in local renal perfusion signals than whole kidney blood flow in anesthetized rats.

SIGNIFICANCE

Combining the detector and laser speckle imaging provides identification of coordination between renal autoregulation mechanisms that is localized in time and space.

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.

Hormonal regulation of salt and water excretion: a mathematical model of whole kidney function and pressure natriuresis

We present a lumped-nephron model that explicitly represents the main features of the underlying physiology, incorporating the major hormonal regulatory effects on both tubular and vascular function, and that accurately simulates hormonal regulation of renal salt and water excretion. This is the first model to explicitly couple glomerulovascular and medullary dynamics, and it is much more detailed in structure than existing whole organ models and renal portions of multiorgan models. In contrast to previous medullary models, which have only considered the antidiuretic state, our model is able to regulate water and sodium excretion over a variety of experimental conditions in good agreement with data from experimental studies of the rat. Since the properties of the vasculature and epithelia are explicitly represented, they can be altered to simulate pathophysiological conditions and pharmacological interventions. The model serves as an appropriate starting point for simulations of physiological, pathophysiological, and pharmacological renal conditions and for exploring the relationship between the extrarenal environment and renal excretory function in physiological and pathophysiological contexts.

Control and modulation of fluid flow in the rat kidney

We have developed a mathematical model of the rat's renal hemodynamics in the nephron level, and used that model to study flow control and signal transduction in the rat kidney. The model represents an afferent arteriole, glomerular filtration, and a segment of a short-loop nephron. The model afferent arteriole is myogenically active and represents smooth muscle membrane potential and electrical coupling. The myogenic mechanism is based on the assumption that the activity of nonselective cation channels is shifted by changes in transmural pressure, such that elevation in pressure induces vasoconstriction, which increases resistance to blood flow. From the afferent arteriole's fluid delivery output, glomerular filtration rate is computed, based on conservation of plasma and plasma protein. Chloride concentration is then computed along the renal tubule based on solute conservation that represents water reabsorption along the proximal tubule and the water-permeable segment of the descending limb, and chloride fluxes driven by passive diffusion and active transport. The model's autoregulatory response is predicted to maintain stable renal blood flow within a physiologic range of blood pressure values. Power spectra associated with time series predicted by the model reveal a prominent fundamental peak at ∼165 mHz arising from the afferent arteriole's spontaneous vasomotion. Periodic external forcings interact with vasomotion to introduce heterodynes into the power spectra, significantly increasing their complexity.

Remanent cell traction force in renal vascular smooth muscle cells induced by integrin-mediated mechanotransduction

It was previously demonstrated in isolated renal vascular smooth muscle cells (VSMCs) that integrin-mediated mechanotransduction triggers intracellular Ca(2+) mobilization, which is the hallmark of myogenic response in VSMCs. To test directly whether integrin-mediated mechanotransduction results in the myogenic response-like behavior in renal VSMCs, cell traction force microscopy was used to monitor cell traction force when the cells were pulled with fibronectin-coated or low density lipoprotein (LDL)-coated paramagnetic beads. LDL-coated beads were used as a control for nonintegrin-mediated mechanotransduction. Pulling with LDL-coated beads increased the cell traction force by 61 ± 12% (9 cells), which returned to the prepull level after the pulling process was terminated. Pulling with noncoated beads had a minimal increase in the cell traction force (12 ± 9%, 8 cells). Pulling with fibronectin-coated beads increased the cell traction force by 56 ± 20% (7 cells). However, the cell traction force was still elevated by 23 ± 14% after the pulling process was terminated. This behavior is analogous to the changes of vascular resistance in pressure-induced myogenic response, in which vascular resistance remains elevated after myogenic constriction. Fibronectin is a native ligand for α(5)β(1)-integrins in VSMCs. Similar remanent cell traction force was found when cells were pulled with beads coated with β(1)-integrin antibody (Ha2/5). Activation of β(1)-integrin with soluble antibody also triggered variations of cell traction force and Ca(2+) mobilization, which were abolished by the Src inhibitor. In conclusion, mechanical force transduced by α(5)β(1)-integrins triggered a myogenic response-like behavior in isolated renal VSMCs.

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.

On the efficacy of the combined use of the cross-bicoherence with surrogate data technique to statistically quantify the presence of nonlinear interactions

The cross-bispectrum is an approach to detect the presence of quadratic phase coupling (QPC) between different components in bivariate signals. Quantification of QPC is by means of the cross-bicoherence index (CBI). The major limitations of the CBI are that it favors only the strongly coupled signals and its accuracy becomes compromised with noise and low coupling strength. To overcome this limitation, a statistical approach which combines CBI with a surrogate data method to determine the statistical significance of the QPC derived from bivariate signals is introduced. We demonstrate the accuracy of the proposed approach using simulation examples which are designed to test its robustness against noise contamination as well as varying levels of phase coupling and data lengths. Comparisons were made to the traditional CBI and the method based on the use of cross-bispectrum followed by a surrogate data technique. Our results show that the cross-bicoherence with surrogate data technique outperforms the two other methods compared in both sensitivity and specificity, and provides an unbiased and statistical approach to determining the presence of QPC in bivariate signals. These results are in contrast to our recent study where the auto-bispectrum combined with surrogate data approach had the best performance. Application of this approach to renal hemodynamic data was applied to renal stop flow pressure data obtained in the nephrons of the normotensive (N = 18) and hypertensive (N = 15) rats. We found significant nonlinear interactions between nephrons only when they are derived from the same cortical renal artery. The accuracy was 100% and verified by comparing the results to the known vascular connectivity between nephrons.

Electrotonic vascular signal conduction and nephron synchronization

Tubuloglomerular feedback (TGF) and the myogenic mechanism control afferent arteriolar diameter in each nephron and regulate blood flow. Both mechanisms generate self-sustained oscillations, the oscillations interact, TGF modulates the frequency and amplitude of the myogenic oscillation, and the oscillations synchronize; a 5:1 frequency ratio is the most frequent. TGF oscillations synchronize in nephron pairs supplied from a common cortical radial artery, as do myogenic oscillations. We propose that electrotonic vascular signal propagation from one juxtaglomerular apparatus interacts with similar signals from other nephrons to produce synchronization. We tested this idea in tubular-vascular preparations from mice. Vascular smooth muscle cells were loaded with a fluorescent voltage-sensitive dye; fluorescence intensity was measured with confocal microscopy. Perfusion of the thick ascending limb activated TGF and depolarized afferent arteriolar smooth muscle cells. The depolarization spread to the cortical radial artery and other afferent arterioles and declined with distance from the perfused juxtaglomerular apparatus, consistent with electrotonic vascular signal propagation. With a mathematical model of two coupled nephrons, we estimated the conductance of nephron coupling by fitting simulated vessel diameters to experimental data. With this value, we simulated nephron pairs to test for synchronization. In single-nephron simulations, the frequency of the TGF oscillation varied with nephron length. Coupling nephrons of different lengths forced TGF frequencies of both pair members to converge to a common value. The myogenic oscillations also synchronized, and the synchronization between the TGF and the myogenic oscillations showed an increased stability against parameter perturbations. Electronic vascular signal propagation is a plausible mechanism for nephron synchronization. Coupling increased the stability of the various oscillations.

Renal blood flow and dynamic autoregulation in conscious mice

Autoregulation of renal blood flow (RBF) occurs via myogenic and tubuloglomerular feedback (TGF) mechanisms that are engaged by pressure changes within preglomerular arteries and by tubular flow and content, respectively. Our understanding of autoregulatory function in the kidney largely stems from experiments in anesthetized animals where renal perfusion pressure is precisely controlled. However, normally occurring variations in blood pressure are sufficient to engage both myogenic and TGF mechanisms, making the assessment of autoregulatory function in conscious animals of significant value. To our knowledge, no studies have evaluated the dynamics of RBF in conscious mice. Therefore, we used spectral analysis of blood pressure and RBF and identified dynamic operational characteristics of the myogenic and TGF mechanisms in conscious, freely moving mice instrumented with ultrasound flow probes and arterial catheters. The myogenic response generates a distinct resonance peak in transfer gain at 0.31 +/- 0.01 Hz. Myogenic-dependent attenuation of RBF oscillations, indicative of active autoregulation, is apparent as a trough in gain below 0.3 Hz (-6.5 +/- 1.3 dB) and a strong positive phase peak (93 +/- 9 deg), which are abolished by amlodipine infusion. Operation of TGF produces a local maximum in gain at 0.05 +/- 0.01 Hz and a positive phase peak (62.3 +/- 12.3 deg), both of which are eliminated by infusion of furosemide. Administration of amlodipine eliminated both myogenic and TGF signature peaks, whereas furosemide shifted the myogenic phase peak to a slower operational frequency. These data indicate that myogenic and TGF dynamics may be used to investigate the effectiveness of renal autoregulatory mechanisms in conscious mice.

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.

Connexins 37 and 40 transduce purinergic signals mediating renal autoregulation

Our previous data indicated that various subtypes of connexin (Cx) were expressed in the juxtaglomerular apparatus. Experiments were performed to characterize the effects on renal autoregulation of specific mimetic peptides that inhibit these Cx subtypes in Wistar-Kyoto rats. Intrarenal infusion of (Cx37,43)GAP27 increased autoregulatory index of renal plasma flow (0.06 +/- 0.05 to 0.47 +/- 0.06, n = 6, P < 0.05) and glomerular filtration rate (GFR; 0.01 +/- 0.07 to 0.49 +/- 0.07, P < 0.05). The additional administration of 8-cyclopentyl- 1,3-dipropylxanthine (CPX) produced a further elevation of autoregulatory index of RPF (0.86 +/- 0.07, P < 0.05) and GFR (0.88 +/- 0.09, P < 0.05), compared with (Cx37,43)GAP27 alone. However, the addition of pyridoxal-phosphate-6-azophenyl-2,4-disulfonic acid (PPADS) to (Cx37,43)GAP27 did not. Combined treatment with CPX and PPADS markedly worsened autoregulatory index of RPF (0.04 +/- 0.10 to 0.81 +/- 0.06, n = 6 P < 0.01) and GFR (0.05 +/- 0.08 to 0.79 +/- 0.05, P < 0.01). (Cx40)GAP27 induced similar changes to (Cx37,43)GAP27. Renal autoregulation was preserved in the presence of (Cx43)GAP26. Our results indicate that the inhibition of gap junction impaired renal autoregulation. Furthermore, the present data provide evidence that both adenosine and purinergic receptors contribute to glomerular autoregulation. Finally, our findings suggest that gap junctions, at least in part, transduce purinergic signals mediating renal autoregulation.

Autonomic nervous nonlinear interactions lead to frequency modulation between low- and high-frequency bands of the heart rate variability spectrum

Cardiac sympathetic and parasympathetic neural activities have been found to interact with each other to efficiently regulate the heart rate and maintain homeostasis. Quantitative and noninvasive methods used to detect the presence of interactions have been lacking, however. This may be because interactions among autonomic nervous systems are nonlinear and nonstationary. The goal of this work was to identify nonlinear interactions between the sympathetic and parasympathetic nervous systems in the form of frequency and amplitude modulations in human heart rate data. To this end, wavelet analysis was performed, followed by frequency analysis of the resultant wavelet decomposed signals in several frequency brackets defined as very low frequency ( f < 0.04 Hz), low frequency (LF; 0.04–0.15 Hz), and high frequency (HF; 0.15–0.4 Hz). Our analysis suggests that the HF band is significantly modulated by the LF band in the heart rate data obtained in both supine and upright body positions. The strength of modulations is stronger in the upright than supine position, which is consistent with elevated sympathetic nervous activities in the upright position. Furthermore, significantly stronger frequency modulation than in the control condition was also observed with the cold pressor test. The results with the cold pressor test, as well as the body position experiments, further demonstrate that the frequency modulation between LF and HF is most likely due to sympathetic and parasympathetic nervous interactions during sympathetic activations. The modulation phenomenon suggests that the parasympathetic nervous system is frequency modulated by the sympathetic nervous system. In this study, there was no evidence of amplitude modulation among these frequencies.

Synchronization among mechanisms of renal autoregulation is reduced in hypertensive rats

We searched for synchronization among autoregulation mechanisms using wavelet transforms applied to tubular pressure recordings in nephron pairs from the surface of rat kidneys. Nephrons have two oscillatory modes in the regulation of their pressures and flows: a faster (100–200 mHz) myogenic mode, and a slower (20–40 mHz) oscillation in tubuloglomerular feedback (TGF). These mechanisms interact; the TGF mode modulates both the amplitude and the frequency of the myogenic mode. Nephrons also communicate with each other using vascular signals triggered by membrane events in arteriolar smooth muscle cells. In addition, the TGF oscillation changes in hypertension to an irregular fluctuation with characteristics of deterministic chaos. The analysis shows that, within single nephrons of normotensive rats, the myogenic mode and TGF are synchronized at discrete frequency ratios, with 5:1 most common. There is no distinct synchronization ratio in spontaneously hypertensive rats (SHR). In normotensive rats, full synchronization of both TGF and myogenic modes is the most probable state for pairs of nephrons originating in a common cortical radial artery. For SHR, full synchronization is less probable; most common in SHR is a state of partial synchronization with entrainment between neighboring nephrons for only one of the modes. Modulation of the myogenic mode by the TGF mode is much stronger in hypertensive than in normotensive rats. Synchronization among nephrons forms the basis for an integrated reaction to blood pressure fluctuations. Reduced synchronization in SHR suggests that the effectiveness of the coordinated response is impaired in hypertension.

Integrin-mediated mechanotransduction in renal vascular smooth muscle cells: activation of calcium sparks

Integrins are transmembrane heterodimeric proteins that link extracellular matrix (ECM) to cytoskeleton and have been shown to function as mechanotransducers in nonmuscle cells. Synthetic integrin-binding peptide triggers Ca2+ mobilization and contraction in vascular smooth muscle cells (VSMCs) of rat afferent arteriole, indicating that interactions between the ECM and integrins modulate vascular tone. To examine whether integrins transduce extracellular mechanical stress into intracellular Ca2+ signaling events in VSMCs, unidirectional mechanical force was applied to freshly isolated renal VSMCs through paramagnetic beads coated with fibronectin (natural ligand of α5β1-integrin in VSMCs). Pulling of fibronectin-coated beads with an electromagnet triggered Ca2+ sparks, followed by global Ca2+ mobilization. Paramagnetic beads coated with low-density lipoprotein, whose receptors are not linked to cytoskeleton, were minimally effective in triggering Ca2+ sparks and global Ca2+ mobilization. Preincubation with ryanodine, cytochalasin-D, or colchicine substantially reduced the occurrence of Ca2+ sparks triggered by fibronectin-coated beads. Binding of VSMCs with antibodies specific to the extracellular domains of α5- and β1-integrins triggered Ca2+ sparks simulating the effects of fibronectin-coated beads. Preincubation of microperfused afferent arterioles with ryanodine or integrin-specific binding peptide inhibited pressure-induced myogenic constriction. In conclusion, integrins transduce mechanical force into intracellular Ca2+ signaling events in renal VSMCs. Integrin-mediated mechanotransduction is probably involved in myogenic response of afferent arterioles.

Effect of tubular inhomogeneities on filter properties of thick ascending limb of Henle's loop

We used a simple mathematical model of rat thick ascending limb (TAL) of the loop of Henle to predict the impact of spatially inhomogeneous NaCl permeability, spatially inhomogeneous NaCl active transport, and spatially inhomogeneous tubular radius on luminal NaCl concentration when sustained, sinusoidal perturbations were superimposed on steady-state TAL flow. A mathematical model previously devised by us that used homogeneous TAL transport and fixed TAL radius predicted that such perturbations result in TAL luminal fluid NaCl concentration profiles that are standing waves. That study also predicted that nodes in NaCl concentration occur at the end of the TAL when the tubular fluid transit time equals the period of a periodic perturbation, and that, for non-nodal periods, sinusoidal perturbations generate non-sinusoidal oscillations (and thus a series of harmonics) in NaCl concentration at the TAL end. In the present study we find that the inhomogeneities transform the standing waves and their associated nodes into approximate standing waves and approximate nodes. The impact of inhomogeneous NaCl permeability is small. However, for inhomogeneous active transport or inhomogeneous radius, the oscillations for non-nodal periods tend to be less sinusoidal and more distorted than in the homogeneous case and to thus have stronger harmonics. Both the homogeneous and non-homogeneous cases predict that the TAL, in its transduction of flow oscillations into concentration oscillations, acts as a low-pass filter, but the inhomogeneities result in a less effective filter that has accentuated non-linearities.

Vascular coupling induces synchronization, quasiperiodicity, and chaos in a nephron tree

The paper presents a study of synchronization phenomena in a system of 22 nephrons supplied with blood from a common cortical radial artery. The nephrons are assumed to interact via hemodynamic and vascularly propagated coupling, both mediated by vascular connections. Using anatomic and physiological criteria, the nephrons are divided into groups: cortical nephrons and medullary nephrons with short, intermediate and long Henle loops. Within each of these groups the delay parameters of the internal feedback regulation are given a random component to represent the internephron variability. For parameters that generate simple limit cycle dynamics in the pressure and flow regulation of single nephrons, the ensemble of coupled nephrons showed steady state, quasiperiodic or chaotic dynamics, depending on the interaction strengths and the arterial blood pressure. When the solutions were either quasiperiodic or chaotic, cortical nephrons synchronized to a single frequency, but the longer medullary nephrons formed two clusters with different frequencies. Under no physiologically realistic combination of parameters did all nephrons assume a common frequency. Our results suggest a greater variability in the nephron dynamics than is apparent from measurements performed on cortical nephrons only. This variability may explain the development of chaotic dynamics in tubular pressure records from hypertensive rats.

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.

Frequency modulation between low- and high-frequency components of the heart rate variability spectrum

Interactions among physiological mechanisms are abundant in biomedical signals, and they may exist to maintain efficient homeostasis. For example, sympathetic and parasympathetic neural activities interact to either elevate or depress the heart rate to maintain homeostasis. There has been considerable effort devoted to developing algorithms that can detect interactions between various physiological mechanisms. However, methods used to detect the presence of interactions between the sympathetic and parasympathetic nervous systems, to take one example, have had limited success. This may be because interactions in physiological systems are non-linear and non-stationary. The goal of this work was to identify non-linear interactions between the sympathetic and parasympathetic nervous systems in the form of frequency and amplitude modulations in human heart-rate data (n=6). To this end, wavelet analysis was performed, followed by frequency analysis of the resultant wavelet decomposed signals in several frequency brackets we define as: very low frequency (f<0.04 Hz), low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz). Our analysis suggests that the high-frequency bracket is modulated by the low-frequency bracket in the heart rate data obtained in both upright and sitting positions. However, there was no evidence of amplitude modulation among these frequencies.

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.

Frequency modulation between low- and high-frequency components of the heart rate variability spectrum may indicate sympathetic-parasympathetic nonlinear interactions

Interactions among physiological mechanisms are abundant in biomedical signals, and they may exist to maintain efficient homeostasis. For example, sympathetic and parasympathetic neural activities interact to either elevate or depress the heart rate, to maintain homeostasis. There has been considerable effort devoted to developing algorithms that can detect interactions between various physiological mechanisms. However, methods used to detect the presence of interactions between the sympathetic and parasympathetic nervous systems, to take one example, have had limited success. This may be because interactions in physiological systems are nonlinear and nonstationary. The goal of this work was to identify nonlinear interactions between the sympathetic and parasympathetic nervous systems in the form of frequency and amplitude modulations in human heart rate data. To this end, wavelet analysis was performed, followed by frequency analysis of the resultant wavelet decomposed signals in several frequency brackets we define as: very low frequency (f<0.04 Hz), low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz). Our analysis suggests that the HF bracket is significantly modulated by the LF bracket in the heart rate data obtained in both supine and upright body positions. Furthermore, the strength of modulations is stronger in the upright than supine position, which is consistent with elevated sympathetic nervous activities in the upright position. However, there was no evidence of amplitude modulation among these frequencies.

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.

Exogenous 5'-nucleotidase improves glomerular autoregulation in Thy-1 nephritic rats

Experiments were performed to characterize renal hemodynamics in Thy-1 nephritic rats. A monoclonal antibody against Thy-1 was intravenously injected to induce mesangiolysis in rats, and 2 days later renal hemodynamic responses to variations in blood pressure were determined. In the first series of experiments, autoregulation of renal plasma flow (RPF) or glomerular filtration rate (GFR) was impaired in nephritic rats. In response to a reduction in blood pressure (98 +/- 2 to 80 +/- 1 mmHg), both RPF (4.17 +/- 0.63 to 3.20 +/- 0.45 ml x min(-1) x g kidney wt(-1), P < 0.05, n = 6) and GFR (0.88 +/- 0.05 to 0.75 +/- 0.06 ml x min(-1).g kidney wt(-1), P < 0.05) were decreased in nephritic rats. Intravenous administration of furosemide and 30% albumin, both of which inhibit tubuloglomerular feedback, diminished renal autoregulation in control but not nephritic rats. In the second studies, the infusion of 5'-nucleotidase, an enzyme expressed on mesangial cells, into a renal artery ameliorated the magnitude of autoregulatory decrements in GFR in nephritic rats (-16 +/- 5 to -6 +/- 2%, P < 0.05, n = 6), but this enzyme failed to alter renal autoregulation in control rats. In the third studies, the effects of indomethacin were examined in nephritic rats. Inhibition of prostaglandin synthesis reduced RPF (4.07 +/- 0.30 to 1.54 +/- 0.22 ml x min(-1) x g kidney wt(-1), P < 0.05, n = 5) and GFR (1.03 +/- 0.18 to 0.69 +/- 0.13 ml x min(-1) x g kidney wt(-1), P < 0.05) in nephritic rats. However, cyclooxygenase inhibition failed to restore renal autoregulation in nephritic rats. Our results indicate that renal autoregulation is impaired in Thy-1 nephritis. Furthermore, the present data provide evidence that prostanoids contribute to maintain renal circulation in nephritic rats. Finally, our findings suggest that mesangial cells and/or 5'-nucleotidase plays an important role in mediating renal autoregulation.

Frequency encoding in renal blood flow regulation

With a model of renal blood flow regulation, we examined consequences of tubuloglomerular feedback (TGF) coupling to the myogenic mechanism via voltage-gated Ca channels. The model reproduces the characteristic oscillations of the two mechanisms and predicts frequency and amplitude modulation of the myogenic oscillation by TGF. Analysis by wavelet transforms of single-nephron blood flow confirms that both amplitude and frequency of the myogenic oscillation are modulated by TGF. We developed a double-wavelet transform technique to estimate modulation frequency. Median value of the ratio of modulation frequency to TGF frequency in measurements from 10 rats was 0.95 for amplitude modulation and 0.97 for frequency modulation, a result consistent with TGF as the modulating signal. The simulation predicted that the modulation was regular, while the experimental data showed much greater variability from one TGF cycle to the next. We used a blood pressure signal recorded by telemetry from a conscious rat as the input to the model. Blood pressure fluctuations induced variability in the modulation records similar to those found in the nephron blood flow results. Frequency and amplitude modulation can provide robust communication between TGF and the myogenic mechanism.