Math @ Duke

Publications [#287305] of Harold Layton
Papers Published
 Layton, HE; Pitman, EB; Moore, LC, Spectral properties of the tubuloglomerular feedback system,
American journal of physiology. Renal physiology, vol. 273 no. 4 424
(1997),
pp. F635F649, ISSN 03636127
(last updated on 2018/05/22)
Abstract: A simple mathematical model was used to investigate the spectral properties of the tubuloglomerular feedback (TGF) system. A perturbation, consisting of smallamplitude broadband forcing, was applied to simulated thick ascending limb (TAL) flow, and the resulting spectral response of the TGF pathway was assessed by computing a power spectrum from resulting TGF regulated TAL flow. Power spectra were computed for both open and closed feedbackloop cases. Openfeedbackloop power spectra are consistent with a mathematical analysis that predicts a nodal pattern in TAL frequency response, with nodes corresponding to frequencies where oscillatory flow has a TAL transit time that equals the steadystate fluid transit time. Closed feedbackloop spectra are dominated by the openloop spectral response, provided that γ, the magnitude of feedback gain is less than the critical value γ(c) required for emergence of a sustained TGFmediated oscillation. For γ exceeding γ(c), closedloop spectra have peaks corresponding to the fundamental frequency of the TGFmediated oscillation and its harmonics. The harmonics, expressed in a nonsinusoidal waveform for tubular flow, are introduced by nonlinear elements of the TGF pathway, notably TAL transit time and the TGF response curve. The effect of transit time on the flow waveform leads to crests that are broader than troughs and to an asymmetry in the magnitudes of increasing and decreasing slopes. For feedback gain magnitude that is sufficiently large, the TGF response curve tends to give a square waveshape to the waveform. Published waveforms and power spectra of in vivo TGF oscillations have features consistent with the predictions of this analysis.


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