Synchronization nephron

Neighboring nephrons also communicate with one another. Experiments performed by Holstein-Rathlou show how nephrons that share a common interlobular artery tend to adjust their TGF mediated pressure oscillations so as to produce a state of in-phase synchronization [7]. Holstein-Rathlou also demonstrated how microperfusion of one nephron (with artificial tubular fluid) affects the amplitude of the pressure oscillation in a neighboring nephron. This provides a method to determine the strength of the nephron-nephron interaction. 

Fig. 12.11 Two-mode oscillatory behavior in the single nephron model. Black colored regions correspond to a chaotic solution. The figure shows different regions in which 1 4, 1 5 and 1 6 synchronization occurs in the interaction between the fast myogenic oscillations...

Fig. 12.12 Internal rotation number as a function of the parameter a calculated from the single-nephron model. Inserts present phase projections for typical regimes. Note how the intra-nephron synchronization is maintained through a complete period-doubling cascade to chaos.

To illustrate the occurrence of intra-nephron synchronization in our experimental results, Fig. 12.13 shows that ratio fsiow/fjast as calculated from the time series in Fig. 12.2c. We still observe a modulation of the fast mode by the slow mode. However, the ratio of the two frequencies maintains a constant value of approximately 1 5 during the entire observation period, i.e., there is no drift of one frequency relative to the other. In full agreement with the predictions of our model, data for other normotensive rats show 1 4 or 1 6 synchronization. Transitions between different states of synchronization obviously represent a major source of complexity in the dynamics of the system. It is possible, for instance, that a nephron can display ei-... 

Let us examine the situation for large values of a where the individual nephron exhibits chaotic dynamics. Figure 12.15a shows a phase plot for one of the nephrons in our two-nephron model for a = 32, T = 16 s, e = 0.0, and y = 0.2. Here we have introduced a slight mismatch AT = 0.2 s in the delay times between the two nephrons and, as illustrated by the tubular pressure variations of Fig. 12.15b, the nephrons follow different trajectories. However, the average period is precisely the same. This is a typical example of phase synchronization of two chaotic oscillators. 

Fig. 12.15 (a) Phase plot for one of the nephrons and (b) temporal variation of the tubular pressures for both nephrons in a pair of coupled chaotically oscillating units, a = 32, T = 16 s, and e = y = 0.2. The figure illustrates the phenomenon of chaotic phase synchronization. By virtue of their mutual coupling the two chaotic oscillators adjust their (average) periods to be identical. The amplitudes, however, vary incoherently and in a chaotic manner [27],... 

Let us consider the case of a = 30 corresponding to a weakly developed chaotic attractor in the individual nephron. The coupling strength y = 0.06 and the delay time T2 in the second nephron is considered as a parameter. Three different chaotic states can be identified in Fig. 12.16. For the asynchronous behavior both of the rotation numbers ns and n f differ from 1 and change continuously with T2. In the synchronization region, the rotation numbers are precisely equal to 1. Here, two cases can be distinguished. To the left, the rotation numbers ns and n/ are both equal to unity and both the slow and the fast oscillations are synchronized. To the right (T2 > 14.2 s), while the slow mode of the chaotic oscillations remain locked, the fast mode drifts randomly. In this case the synchronization condition is fulfilled only for one of oscillatory modes, and we speak of partial synchronization. A detailed analysis of the experimental data series reveals precisely the same phenomena [31]. 

Fig. 12.16 Full and partial synchronization of the fast and slow motions between two interacting nephrons (/ = 13.5 s, a = 30.0 and y = 0.06). Full synchronization is realized when both the fast nj and slow ns rotation numbers equal to 1. To the right in the figure there is an interval where only the slow modes are synchronized. The delay / in the loop of Henle for the second nephron is used as a parameter.

Figure 12.17 shows an example of the tubular pressure variations that one can observe for adjacent nephrons for a normotensive rat. For one of the nephrons, the pressure variations are drawn in black, and for the other nephron in gray. Both curves show fairly regular variations in the tubular pressures with a period of approximately 31s. The amplitude is about 1.5 mmHg and the mean pressure is close to 13 mmHg. Inspection of the figure clearly reveals that the oscillations are synchronized and remain nearly in phase for the entire observation period (corresponding to 25 periods of oscillation). 

Figures 12.18a and b show examples of the tubular pressure variations in pairs of neighboring nephrons for hypertensive rats. These oscillations are significantly more irregular than the oscillations displayed in Fig. 12.17 and, as previously discussed, it is likely that they can be ascribed to a chaotic dynamics. In spite of this irregularity, however, one can visually observe a certain degree of synchronization between the interacting nephrons.

Fig. 12.18 Two examples (a and b) of the tubular pressure variations that one can observe in adjacent nephrons for hypertensive rats. In spite of the irregularity in the dynamics, one can see a certain degree of synchronization in the phases of the two oscillations. This synchronization is supported by formal investigations, e.g., by means of the wavelet technique.

In a recent study [34], we made use of wavelet and double-wavelet analysis to examine the relative occurrence of various states of synchronization in pairs of interacting nephrons. We showed that both full and partial synchronization occur for normotensive as well as for hypertensive rats, and that the partial synchronization can involve only the slow oscillations or only the fast oscillations. We also used... 

In order to examine the synchronization phenomena that can arise in larger ensembles of nephrons, we recently developed a model of a vascular-coupled nephron tree [35], focusing on the effect of the hemodynamic coupling. As explained above, the idea is here that, as one nephron reduces its arterioler diameter to lower the incoming blood flow, more blood is distributed to the other nephrons in accordance with the flow resistances in the network. An interesting aspect of this particular coupling is that the nephrons interact both via the blood flow that controls their tendency to oscillate and via the oscillations in this blood flow that control their tendency to synchronize. We refer to such a structure as a resource distribution chain, and we have shown that phenomena similar to those that we describe here... 

In collaboration with Alexander Gorbach, NIH, we have initiated a study of the spatial patterns in the nephron synchronization. This study involves the use of infrared cameras or other types of equipment that can measure variations in the blood supply by small (0.01°C) fluctuations in the temperature at the surface of the kidney. It is also of interest to study how the large amplitude oscillations in pressure, fluid flow, and salt concentration at the entrance of the distal tubule influence the delicate hormonal processes in that part of the kidney, to establish a more quantitative description of some of the mechanisms involved in the development of hypertension, and to examine the effects of various drugs. 

N.-H. Holstein-Rathlou, Synchronization of Proximal Intratubular Pressure Oscillations Evidence for Interaction between Nephrons, Pflugers Archiv 408,438-443 (1987). 

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