Coupling-induced complexity in nephron models of renal blood flow regulation

Abstract

Laugesen JL, Sosnovtseva OV, Mosekilde E, Holstein-Rathlou N, Marsh DJ. Coupling-induced complexity in nephron models of renal blood flow regulation. Am J Physiol Regul Integr Comp Physiol 298: R997-R1006, 2010. First published February 10, 2010 doi:10.1152/ajpregu.00714.2009.-Tubular pressure and nephron blood flow time series display two interacting oscillations in rats with normal blood pressure. Tubuloglomerular feedback (TGF) senses NaCl concentration in tubular fluid at the macula densa, adjusts vascular resistance of the nephron's afferent arteriole, and generates the slower, larger-amplitude oscillations (0.02-0.04 Hz). The faster smaller oscillations (0.1-0.2 Hz) result from spontaneous contractions of vascular smooth muscle triggered by cyclic variations in membrane electrical potential. The two mechanisms interact in each nephron and combine to act as a high-pass filter, adjusting diameter of the afferent arteriole to limit changes of glomerular pressure caused by fluctuations of blood pressure. The oscillations become irregular in animals with chronic high blood pressure. TGF feedback gain is increased in hypertensive rats, leading to a stronger interaction between the two mechanisms. With a mathematical model that simulates tubular and arteriolar dynamics, we tested whether an increase in the interaction between TGF and the myogenic mechanism can cause the transition from periodic to irregular dynamics. A one-dimensional bifurcation analysis, using the coefficient that couples TGF and the myogenic mechanism as a bifurcation parameter, shows some regions with chaotic dynamics. With two nephrons coupled electrotonically, the chaotic regions become larger. The results support the hypothesis that increased oscillator interactions contribute to the transition to irregular fluctuations, especially when neighboring nephrons are coupled, which is the case in vivo. renal autoregulation; nonlinear dynamics; tubuloglomerular feedback; myogenic mechanism; chaos TWO MECHANISMS, TUBULOGLOMERULAR feedback (TGF) and the myogenic mechanism, operate in each nephron of mammalian kidneys to regulate blood flow when arterial blood pressure changes (14 -16, 22, 44). Each mechanism is potentially unstable and operates in a nonlinear regime: TGF oscillates at 0.02-0.04 Hz and the myogenic mechanism at 0.1-0.2 Hz. The TGF oscillation is the more pronounced. These mechanisms interact because they operate simultaneously on the contractile machinery of vascular smooth muscle cells. The interaction leads to modulation of the amplitude and frequency of the myogenic oscillation by TGF, a finding predicted by a mathematical model (26) and confirmed in experimental measurements (28).The dynamics of the TGF-myogenic ensemble undergo a transition in rats with either a genetic or a renovascular form of hypertension to a state with characteristics of deterministic chaos (51). Lyapunov exponents are positive; the phase space attractor constructed from the data is low dimensional and has a noninteger correlation dimension (51); surrogat...

Multinephron dynamics on the renal vascular network

“…In the renal vascular network, these interactions arise among nephrons because TGF and the myogenic mechanism develop self-sustained oscillations. Over time periods of 30 min or longer the oscillations are made irregular by blood pressure fluctuations (13,28) and by intrinsic factors, like deterministic chaos (21,30,48,49,51). We evaluated phase locking between pairs of nephrons to estimate the extent of synchronization.…”

“…As a part of the two-point approximation, the effect of the TGF signal in the segment farther from the glomerulus was 0.33 of the effect in the nearer segment; the two segments were made to interact through an electrical conductance between them. The details of these model components, including the parameter values, have been published in a number of studies, most recently in Marsh et al (32); a causal model diagram is in Laugesen et al (21) and is reproduced here as Fig. 2.…”

“…Two potential sources of this change have been identified: an increase in TGF gain (8,27) and an increase in the electrotonic conductance between nephrons (6,47). Simulations with nephron models show that each independently supports the change in dynamics observed in hypertension (21,30). The network model will permit us to evaluate the relative importance of each and the interaction between them.…”

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.…”

“…Over the years we have developed a number of different models of the regulation of the afferent blood Àow by the individual nephron, each emphasizing a speci¿c aspect of the problem such as the absorption of water and salts along the loop of Henle [48] or the interaction between the macula densa cells and the smooth muscle cells in the arteriolar wall [36]. In the present survey we will consider the model described by Barfred et al [49].…”