Double-wavelet approach to studying the modulation properties of nonstationary multimode dynamics

Interacting information streams on the nephron arterial network

Blood flow and glomerular filtration in the kidney are regulated by two mechanisms acting on the afferent arteriole of each nephron. The two mechanisms operate as limit cycle oscillators, each responding to a different signal. The myogenic mechanism is sensitive to a transmural pressure difference across the wall of the arteriole, and tubuloglomerular feedback (TGF) responds to the NaCl concentration in tubular fluid flowing into the nephron's distal tubule,. The two mechanisms interact with each other, synchronize, cause oscillations in tubular flow and pressure, and form a bimodal electrical signal that propagates into the arterial network. The electrical signal enables nephrons adjacent to each other in the arterial network to synchronize, but non-adjacent nephrons do not synchronize. The arteries supplying the nephrons have the morphologic characteristics of a rooted tree network, with 3 motifs characterizing nephron distribution. We developed a model of 10 nephrons and their afferent arterioles in an arterial network that reproduced these structural characteristics, with half of its components on the renal surface, where experimental data suitable for model validation is available, and the other half below the surface, from which no experimental data has been reported. The model simulated several interactions: TGF-myogenic in each nephron with TGF modulating amplitude and frequency of the myogenic oscillation; adjacent nephron-nephron with strong coupling; non-adjacent nephron-nephron, with weak coupling because of electrical signal transmission through electrically conductive arterial walls; and coupling involving arterial nodal pressure at the ends of each arterial segment, and between arterial nodes and the afferent arterioles originating at the nodes. The model predicted full synchronization between adjacent nephrons pairs and partial synchronization among weakly coupled nephrons, reproducing experimental findings. The model also predicted aperiodic fluctuations of tubular and arterial pressures lasting longer than TGF oscillations in nephrons, again confirming experimental observations. The model did not predict complete synchronization of all nephrons.

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.

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.

Detection of low-frequency oscillations in renal blood flow

Detection of the low-frequency (LF; ∼0.01 Hz) component of renal blood flow, which is theorized to reflect the action of a third renal autoregulatory mechanism, has been difficult due to its slow dynamics. In this work, we used three different experimental approaches to detect the presence of the LF component of renal autoregulation using normotensive and spontaneously hypertensive rats (SHR), both anesthetized and unanesthetized. The first experimental approach utilized a blood pressure forcing in the form of a chirp, an oscillating perturbation with linearly increasing frequency, to elicit responses from the LF autoregulatory component in anesthetized normotensive rats. The second experimental approach involved collection and analysis of spontaneous blood flow fluctuation data from anesthetized normotensive rats and SHR to search for evidence of the LF component in the form of either amplitude or frequency modulation of the myogenic and tubuloglomerular feedback mechanisms. The third experiment used telemetric recordings of arterial pressure and renal blood flow from normotensive rats and SHR for the same purpose. Our transfer function analysis of chirp signal data yielded a resonant peak centered at 0.01 Hz that is greater than 0 dB, with the transfer function gain attenuated to lower than 0 dB at lower frequencies, which is a hallmark of autoregulation. Analysis of the data from the second experiments detected the presence of ∼0.01-Hz oscillations only with isoflurane, albeit at a weaker strength compared with telemetric recordings. With the third experimental approach, the strength of the LF component was significantly weaker in the SHR than in the normotensive rats. In summary, our detection via the amplitude modulation approach of interactions between the LF component and both tubuloglomerular feedback and the myogenic mechanism, with the LF component having an identical frequency to that of the resonant gain peak, provides evidence that 0.01-Hz oscillations may represent the third autoregulatory mechanism.

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.

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.

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.

A novel mechanism of renal blood flow autoregulation and the autoregulatory role of A1 adenosine receptors in mice

Autoregulation of renal blood flow (RBF) is mediated by a fast myogenic response (MR; approximately 5 s), a slower tubuloglomerular feedback (TGF; approximately 25 s), and potentially additional mechanisms. A1 adenosine receptors (A1AR) mediate TGF in superficial nephrons and contribute to overall autoregulation, but the impact on the other autoregulatory mechanisms is unknown. We studied dynamic autoregulatory responses of RBF to rapid step increases of renal artery pressure in mice. MR was estimated from autoregulation within the first 5 s, TGF from that at 5-25 s, and a third mechanism from 25-100 s. Genetic deficiency of A1AR (A1AR-/-) reduced autoregulation at 5-25 s by 50%, indicating a residual fourth mechanism resembling TGF kinetics but independent of A1AR. MR and third mechanism were unaltered in A1AR-/-. Autoregulation in A1AR-/- was faster at 5-25 than at 25-100 s suggesting two separate mechanisms. Furosemide in wild-type mice (WT) eliminated the third mechanism and enhanced MR, indicating TGF-MR interaction. In A1AR-/-, furosemide did not further impair autoregulation at 5-25 s, but eliminated the third mechanism and enhanced MR. The resulting time course was the same as during furosemide in WT, indicating that A1AR do not affect autoregulation during furosemide inhibition of TGF. We conclude that at least one novel mechanism complements MR and TGF in RBF autoregulation, that is slower than MR and TGF and sensitive to furosemide, but not mediated by A1AR. A fourth mechanism with kinetics similar to TGF but independent of A1AR and furosemide might also contribute. A1AR mediate classical TGF but not TGF-MR interaction.

Using wavelet analysis to detect the influence of low frequency magnetic fields on human physiological tremor

The influence of extremely low frequency magnetic fields (ELF-MFs) on human physiological processes and, in particular, on motor activity is still not established with certainty. Using the wavelet-transform approach, changes in the characteristics of human finger micromovement are studied in the presence of a low intensity MF centred at the level of the head. Different approaches to nonstationary signal analysis involving real as well as complex wavelet functions are considered. We find evidence that ELF-MFs lead to more regular postural tremor and more homogeneous energy distribution.

Use of wavelet and fast Fourier transforms in pharmacodynamics

Progress has been made in the development and application of mechanism-based pharmacodynamic models for describing the drug-specific and physiological factors influencing the time course of responses to the diverse actions of drugs. However, the biological variability in biosignals and the complexity of pharmacological systems often complicate or preclude the direct application of traditional structural and nonstructural models. Mathematical transforms may be used to provide measures of drug effects, identify structural and temporal patterns, and visualize multidimensional data from analyses of biomedical signals and images. Fast Fourier transform (FFT) and wavelet analyses are two methodologies that have proven to be useful in this context. FFT converts a signal from the time domain to the frequency domain, whereas wavelet transforms colocalize in both domains and may be utilized effectively for nonstationary signals. Nonstationary drug effects are common but have not been well analyzed and characterized by other methods. In this review, we discuss specific applications of these transforms in pharmacodynamics and their potential role in ascertaining the dynamics of spatiotemporal properties of complex pharmacological systems.