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Parameter estimation of feedback gain in a stochastic model of renal hemodynamics: differences between spontaneously hypertensive and Sprague-Dawley rats

Departments of ¹Biostatistics and ⁴Medical Physiology, University of Copenhagen, Copenhagen, Denmark; ²Department of Physiology and Biophysics, University of South Florida, Tampa, Florida; and ³Department of Molecular Pharmacology, Physiology, and Biotechnology, Brown University, Providence, Rhode Island

Submitted 28 June 2005 ; accepted in final form 29 September 2006

Proximal tubular pressure shows periodic self-sustained oscillations in normotensive rats but highly irregular fluctuations in spontaneously hypertensive rats (SHR). Although we have suggested that the irregular fluctuations in SHR represent low-dimensional deterministic chaos in tubuloglomerular feedback (TGF), they could also arise from other mechanisms, such as intrinsic instabilities in preglomerular vessels or inputs from neighboring, coupled nephrons. To test this possibility, we applied a parameter estimation procedure to a model of TGF, where a stochastic process was added to represent mechanisms not included explicitly in the model. In its deterministic version, the model can have chaotic dynamics arising from TGF. The model introduces random fluctuations into a parameter that determines the gain of TGF. The model shows a rich variety of dynamics ranging from low-dimensional deterministic oscillations and chaos to high-dimensional random fluctuations. To fit the data from normotensive rats, the model must introduce only a small variation in the feedback gain, and its estimates of that gain agree well with experimental values. These results support the use of the deterministic model of nephron dynamics in normotensive rats. In contrast, the irregular tubular pressure fluctuations in SHR were best described by a model dominated by random parameter fluctuations. The results point to the failure of simple mathematical models of nephron dynamics adequately to describe processes that are important for the irregular tubular pressure fluctuations and the need to consider other factors, such as differences in vascular function or nephron-nephron interactions, in further work on this problem.

stochastic processes; spectral density; nephron; tubuloglomerular feedback mechanism; deterministic chaos

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