TY - JOUR

T1 - Parameter estimation in a stochastic model of the tubuloglomerular feedback mechanism in a rat nephron.

AU - Ditlevsen, Susanne

AU - Yip, Kay-Pong

AU - Holstein-Rathlou, N.-H.

N1 - Keywords: Animals; Computer Simulation; Feedback; Glomerular Filtration Rate; Kidney Glomerulus; Kidney Tubules; Male; Models, Biological; Nephrons; Rats; Rats, Sprague-Dawley; Renal Circulation; Stochastic Processes

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

U2 - 10.1016/j.mbs.2004.12.007

DO - 10.1016/j.mbs.2004.12.007

M3 - Journal article

C2 - 15836864

VL - 194

SP - 49

EP - 69

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 1

ER -