Parameter estimation in a stochastic model of the tubuloglomerular feedback mechanism in a rat nephron

• Published in: Mathematical biosciences Vol. 194; no. 1; pp. 49 - 69
• Main Authors: Ditlevsen, Susanne, Yip, Kay-Pong, Holstein-Rathlou, Niels-Henrik
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.03.2005
• Subjects: Animals; Computer Simulation; Feedback - physiology; Glomerular Filtration Rate - physiology; Kidney Glomerulus - physiology; Kidney Tubules - physiology; Male; Models, Biological; Myogenic response; Nephrons - physiology; Parameter estimation; Rat kidney; Rats; Rats, Sprague-Dawley; Renal Circulation - physiology; Spectral density; Stochastic differential equations; Stochastic Processes; Tubuloglomerular feedback mechanism; Myogenic response; Parameter estimation; Stochastic differential equations; Tubuloglomerular feedback mechanism; Spectral density; Rat kidney
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/j.mbs.2004.12.007

A key parameter in the understanding of renal hemodynamics is the gain of the feedback function in the tubuloglomerular feedback mechanism. A dynamic model of autoregulation of renal blood flow and glomerular filtration rate has been extended to include a stochastic differential equations model of one of the main parameters that determines feedback gain. The model reproduces fluctuations and irregularities in the tubular pressure oscillations that the former deterministic models failed to describe. This approach assumes that the gain exhibits spontaneous erratic variations that can be explained by a variety of influences, which change over time (blood pressure, hormone levels, etc.). To estimate the key parameters of the model we have developed a new estimation method based on the oscillatory behavior of the data. The dynamics is characterized by the spectral density, which has been estimated for the observed time series, and numerically approximated for the model. The parameters have then been estimated by the least squares distance between data and model spectral densities. To evaluate the estimation procedure measurements of the proximal tubular pressure from 35 nephrons in 16 rat kidneys have been analyzed, and the parameters characterizing the gain and the delay have been estimated. There was good agreement between the estimated values, and the values obtained for the same parameters in independent, previously published experiments.