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

Abstract

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.

Synchronization of period-doubling oscillations in vascular coupled nephrons

“…The response time of the TGF mechanism is restricted by the time it takes the tubular fluid to flow through the loop of Henle, and the system presumably achieves the fastest possible response by adopting an oscillatory mode of regulation. As described in previous work, 23,24 interaction between adjacent nephrons leads to synchronization of their pressure oscillations. Experimentally, one typically observes that the tubular pressures in a pair of neighboring nephrons oscillate in synchrony for a period of 20-40 min, lose synchrony for a while and then synchronize again.…”

“…22 These two mechanisms tend to synchronize the pressure oscillations of the interacting nephrons, typically such that either in-phase or antiphase operation is observed. 23,24 The purpose of the present paper is to examine the transitions in and out of synchrony that occur through interaction between a pair of neighboring nephrons. The classical theory of synchronization 25 considers a system of two interacting limit cycle oscillators (or a single oscillator subjected to an external periodic forcing).…”

Electrotonic vascular signal conduction and nephron synchronization

“…The simulated nephrons included a majority of cortical nephrons and smaller numbers of medullary nephrons (22). The model used to simulate each nephron (1) was much simpler than the one used in this study, had no myogenic mechanism, and modeled coupling phenomenologically, without specifying a mechanism.…”

The transition to chaotic phase synchronization

“…As part of an effort to understand the relation between hypertension and kidney function we have long been engaged with a study of nephron autoregulation, i.e., of the mechanisms by which the individual functional unit of the kidney regulates the incoming blood Àow in response to variations in the arterial blood pressure [34,35,36]. This regulation involves two different mechanisms: A myogenic mechanism that reacts directly to changes in the arterial pressure, and a so-called tubuloglomerular feedback (TGF) mechanism that responds to signals from specialized cells (the macula densa cells) near the terminal part of the loop of Henle.…”