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Control and Modulation of Fluid Flow in the Rat Kidney

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Abstract

We have developed a mathematical model of the rat’s renal hemodynamics in the nephron level, and used that model to study flow control and signal transduction in the rat kidney. The model represents an afferent arteriole, glomerular filtration, and a segment of a short-loop nephron. The model afferent arteriole is myogenically active and represents smooth muscle membrane potential and electrical coupling. The myogenic mechanism is based on the assumption that the activity of nonselective cation channels is shifted by changes in transmural pressure, such that elevation in pressure induces vasoconstriction, which increases resistance to blood flow. From the afferent arteriole’s fluid delivery output, glomerular filtration rate is computed, based on conservation of plasma and plasma protein. Chloride concentration is then computed along the renal tubule based on solute conservation that represents water reabsorption along the proximal tubule and the water-permeable segment of the descending limb, and chloride fluxes driven by passive diffusion and active transport. The model’s autoregulatory response is predicted to maintain stable renal blood flow within a physiologic range of blood pressure values. Power spectra associated with time series predicted by the model reveal a prominent fundamental peak at ∼165 mHz arising from the afferent arteriole’s spontaneous vasomotion. Periodic external forcings interact with vasomotion to introduce heterodynes into the power spectra, significantly increasing their complexity.

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Acknowledgements

This research was supported, in part, by the National Institutes of Health, National Institute of Diabetes and Digestive and Kidney Diseases, via grant DK089066.

Portions of this work were presented at Experimental Biology 2012 (FASEB J. 26:690.2, 2012).

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  1. Department of Mathematics, Duke University, Box 90320, Durham, NC, 27708-0320, USA

    Ioannis Sgouralis & Anita T. Layton

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  1. Ioannis Sgouralis
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  2. Anita T. Layton
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Correspondence to Ioannis Sgouralis.

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Sgouralis, I., Layton, A.T. Control and Modulation of Fluid Flow in the Rat Kidney. Bull Math Biol 75, 2551–2574 (2013). https://doi.org/10.1007/s11538-013-9907-5

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