Characterizing multimode interaction in renal autoregulation

Abstract

The purpose of this paper is to demonstrate how modern statistical techniques of non-stationary time-series analysis can be used to characterize the mutual interaction among three coexisting rhythms in nephron pressure and flow regulation. Besides a relatively fast vasomotoric rhythm with a period of 5-8 s and a somewhat slower mode arising from an instability in the tubuloglomerular feedback mechanism, we also observe a very slow mode with a period of 100-200 s. Double-wavelet techniques are used to study how the very slow rhythm influences the two faster modes. In a broader perspective, the paper emphasizes the significance of complex dynamic phenomena in the normal and pathological function of physiological systems and discusses how simulation methods can help to understand the underlying biological mechanisms. At the present there is no causal explanation of the very slow mode. However, vascular oscillations with similar frequencies have been observed in other tissues.

Multinephron dynamics on the renal vascular network

“…Each nephron, regardless of its own length, developed complex blood flow dynamics. Synchronization of TGF with myogenic dynamics in individual nephrons was not preserved and fluctuations at frequencies lower than that of TGF emerged, a result consistent with experimental observations (36,41). Synchronization among nephrons varied inversely with the number of nodes of separation, and, as might be expected, synchronization of electrical events among nodes of the vascular network was weaker in the asymmetric configuration than in the symmetric one, as shown in Supplemental Videos S1 and S2.…”

“…The individual nephrons in a network do not undergo these changes simultaneously, and neither in the network nor individual nephrons are these changes periodic. Siu et al (42) reported 10-mHz oscillations in rat whole kidney blood flow, and Pavlov et al (36) detected oscillations in proximal tubule hydrostatic pressure at a similar frequency, also in rats. In both reports, the spontaneous low-frequency activity was small in normotensive animals and enhanced by forcing renal artery pressure over a range of frequencies (42).…”

“…Low-frequency fluctuations have been described in experimental time series (36,42), but no mechanism has been suggested. Our results support the hypothesis that network dynamics are responsible.…”

“…There is a slower change in proximal tubular pressure and renal blood flow, but no separate mechanism has been identified as its cause (36,42).…”

C-type period-doubling transition in nephron autoregulation

“…The saddle-node bifurcation curve SN 4 that delineates the region of stable period-4 dynamics arises from a point on the stable branch of PD 2 . The saddle-node bifurcation curve SN 8 hereafter emerges from a point on the unstable branch of PD 4 , and the saddle-node bifurcation curve SN 16 emerges from a point on the stable branch of PD 8 . In general, we find that the point of emergence for a new saddlenode bifurcation curve tends to alternate through the period-doubling cascade between the stable and unstable branches of the period-doubling curves.…”