Synchronization phenomena in nephron–nephron interaction

Abstract

Experimental data for tubular pressure oscillations in rat kidneys are analyzed in order to examine the different types of synchronization that can arise between neighboring functional units. For rats with normal blood pressure, the individual unit ͑the nephron͒ typically exhibits regular oscillations in its tubular pressure and flow variations. For such rats, both in-phase and antiphase synchronization can be demonstrated in the experimental data. For spontaneously hypertensive rats, where the pressure variations in the individual nephrons are highly irregular, signs of chaotic phase and frequency synchronization can be observed. Accounting for a hemodynamic as well as for a vascular coupling between nephrons that share a common interlobular artery, we develop a mathematical model of the pressure and flow regulation in a pair of adjacent nephrons. We show that this model, for appropriate values of the parameters, can reproduce the different types of experimentally observed synchronization. © 2001 American Institute of Physics. ͓DOI: 10.1063/1.1376398͔The kidneys play an essential role in regulating the blood pressure and maintaining a proper environment for the cells of the body. This control depends to a large extent on mechanisms associated with the individual functional unit, the nephron. However, a variety of cooperative phenomena that arise from interactions among the nephrons may also be important. In-phase synchronization, for instance, where the nephrons simultaneously perform the same regulatory adjustments of the incoming blood flow is likely to produce fast and strong effects in the overall response to changes in the external conditions. Out-ofphase synchronization, on the other hand, will lead to a slower and less pronounced response of the system in the aggregate. The purpose of the present paper is to demonstrate how different forms of synchronization can be observed in the pressure and flow variations for neighboring nephrons. Particularly interesting is the observation of chaotic phase synchronization in rats with high blood pressure. Based on a description of the physiological mechanisms involved in the various regulations, we develop a mathematical model that can account for the experimentally observed synchronization phenomena.

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

“…2͑a͒, are the same as have been reported previously. 5,14,19,25 The tubule pressure and the arteriolar diameter oscillate, and the motion on the phase plane is that of a limit cycle oscillator. Parameters have been chosen that are typical of measurements made in normal animals.…”

“…The model has been described and evaluated in detail in other studies, 5,14,19,20,25 and is presented unmodified in the Appendix. The model consists of a set of five coupled ordinary differential equations.…”

“…Nephrons also communicate with each other by means of vascular signaling initiated by the TGF mechanism and propagated electrotonically and decrementally over the vascular wall. [3][4][5][6] Both TGF regulation and the myogenic mechanism are oscillating nonlinear systems that interact with each other within single nephrons 3,[7][8][9][10][11][12][13] and, by virtue of the vascularly propagated signals, between neighboring nephrons. 14,15 These interactions produce modulation of the myogenic mechanism by TGF as well as different forms of synchronization.…”

The transition to chaotic phase synchronization

“…Chaotic phase synchronization has been observed in a broad range of different physical, technical and biological systems, including a plasma discharge tube paced with a low amplitude wave generator [8], an array of coupled electronic oscillators [9], and a pair of interacting functional units of the kidney [10]. The transition between phase-locked and un-locked states represents a signi¿cant change in behavior, and we have previously suggested that transitions between different synchronization states among oscillatory biological processes may represent an important component in the normal physiological regulation of the living organism [10].…”

“…The transition between phase-locked and un-locked states represents a signi¿cant change in behavior, and we have previously suggested that transitions between different synchronization states among oscillatory biological processes may represent an important component in the normal physiological regulation of the living organism [10].…”