Bifurcation analysis of nephron pressure and flow regulation

One- and two-dimensional continuation techniques are applied to study the bifurcation structure of a model of renal flow and pressure control. Integrating the main physiological mechanisms by which the individual nephron regulates the incoming blood flow, the model describes the interaction between the tubuloglomerular feedback and the response of the afferent arteriole. It is shown how a Hopf bifurcation leads the system to perform self-sustained oscillations if the feedback gain becomes sufficiently strong, and how a further increase of this parameter produces a folded structure of overlapping period-doubling cascades. Similar phenomena arise in response to increasing blood pressure. The numerical analyses are supported by existing experimental results on anesthetized rats. (c) 1996 American Institute of Physics.     

Synchronization phenomena in nephron-nephron interaction

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 nephron) 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. (c) 2001 American Institute of Physics.     

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.     

SENSITIZED TRIPLET FORMATION OF CHLOROPHYLL-A AND ß-CAROTENE

The naphthalene-sensitized formation of triplet excited chlorophyll-a (Chl-a) and all-transß-carotene has been studied by pulse radiolysis. The rate constants for transfer of triplet energy from naphthalene to Chl-a and all-transß-carotene in benzene at 25°C are (3.6 ± 0.6)·10⁹M^-1 s^-1 and (10.7 ± 1.2)·10⁹M^-1 s^-1, respectively. The decays of the excited triplet states of naphthalene, Chl-a and all-transß-carotene all follow a mixed first-and second-order mechanism. The first-order rate constant for triplet decay is strongly dose dependent for naphthalene but only slightly dependent and independent of dose for Chl-a and all-transß-carotene, respectively. The rate constants for triplet-triplet annihilation are (1.4 ± 0.3)·10⁹M^-1 s^-1 for Chl-a and (3.6 ± 0.4)·10⁹M^-1 s^-1 for all-transß carotene. The nearly constant ratio k(ß-carotene)/k(Chl-a) for the bimolecular triplet energy transfer rate constants is discussed in terms of the molecular shapes of the two molecules. The energetics of the triplet-triplet annihilation of all-transß-carotene are discussed, and it is proposed that production of the excited ¹A_B state may be a major route in the annihilation process.